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onewheelskyward/xml

Created February 20, 2020 00:02
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xml
<?xml version='1.0' encoding='UTF-8'?>
<queryresult success='true'
error='false'
numpods='16'
datatypes=''
timedout=''
timedoutpods=''
timing='6.764'
parsetiming='0.228'
parsetimedout='false'
recalculate=''
id='MSP487523h005d7ihcg97g200002d298c6db0i6i3f0'
host='https://www5a.wolframalpha.com'
server='24'
related='https://www5a.wolframalpha.com/api/v1/relatedQueries.jsp?id=MSPa487623h005d7ihcg97g2000053563e7ebg8g7e3e5106314412482791943'
version='2.6'>
<pod title='Input'
scanner='Identity'
id='Input'
position='100'
error='false'
numsubpods='1'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP487723h005d7ihcg97g200005fb800g9e53hc71d?MSPStoreType=image/gif&amp;s=24'
alt='sin(x)'
title='sin(x)'
width='35'
height='18'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x)</plaintext>
</subpod>
<expressiontypes count='1'>
<expressiontype name='Default' />
</expressiontypes>
</pod>
<pod title='Plots'
scanner='Plotter'
id='Plot'
position='200'
error='false'
numsubpods='2'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP487823h005d7ihcg97g200003g3c2c7bh74b2d5c?MSPStoreType=image/gif&amp;s=24'
alt='Plots'
title=''
width='335'
height='145'
type='2DMathPlot_1'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext></plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP487923h005d7ihcg97g2000012bd68c401b31304?MSPStoreType=image/gif&amp;s=24'
alt='Plots'
title=''
width='349'
height='146'
type='2DMathPlot_1'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext></plaintext>
</subpod>
<expressiontypes count='2'>
<expressiontype name='2DMathPlot' />
<expressiontype name='2DMathPlot' />
</expressiontypes>
</pod>
<pod title='Alternate form'
scanner='Simplification'
id='AlternateForm'
position='300'
error='false'
numsubpods='1'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488023h005d7ihcg97g2000064cfhd52ieicchb8?MSPStoreType=image/gif&amp;s=24'
alt='1/2 i e^(-i x) - 1/2 i e^(i x)'
title='1/2 i e^(-i x) - 1/2 i e^(i x)'
width='105'
height='36'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>1/2 i e^(-i x) - 1/2 i e^(i x)</plaintext>
</subpod>
<expressiontypes count='1'>
<expressiontype name='Default' />
</expressiontypes>
</pod>
<pod title='Roots'
scanner='Reduce'
id='SymbolicSolution'
position='400'
error='false'
numsubpods='1'
primary='true'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488123h005d7ihcg97g200004if459b2g1ha07g3?MSPStoreType=image/gif&amp;s=24'
alt='x = π n, n element Z'
title='x = π n, n element Z'
width='550'
height='22'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>x = π n, n element Z</plaintext>
</subpod>
<expressiontypes count='1'>
<expressiontype name='Default' />
</expressiontypes>
<states count='2'>
<state name='Approximate form'
input='SymbolicSolution__Approximate form' />
<state name='Step-by-step solution'
input='SymbolicSolution__Step-by-step solution'
stepbystep='true' />
</states>
<infos count='1'>
<info text='Z is the set of integers'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488223h005d7ihcg97g2000019b65efcbc958bi5?MSPStoreType=image/gif&amp;s=24'
alt='Z is the set of integers'
title='Z is the set of integers'
width='144'
height='18' />
<link url='http://reference.wolfram.com/language/ref/Integers.html'
text='Documentation'
title='Documentation' />
<link url='http://mathworld.wolfram.com/Z.html'
text='Definition'
title='MathWorld' />
</info>
</infos>
</pod>
<pod title='Properties as a real function'
scanner='FunctionProperties'
id='PropertiesAsARealFunction'
position='500'
error='false'
numsubpods='4'>
<subpod title='Domain'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488323h005d7ihcg97g200003086c9gih0f80552?MSPStoreType=image/gif&amp;s=24'
alt='R (all real numbers)'
title='R (all real numbers)'
width='134'
height='18'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>R (all real numbers)</plaintext>
</subpod>
<subpod title='Range'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488423h005d7ihcg97g200001ha082522hbeecde?MSPStoreType=image/gif&amp;s=24'
alt='{y element R : -1&lt;=y&lt;=1}'
title='{y element R : -1&lt;=y&lt;=1}'
width='122'
height='18'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>{y element R : -1&lt;=y&lt;=1}</plaintext>
</subpod>
<subpod title='Periodicity'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488523h005d7ihcg97g2000060f1ic44cai41581?MSPStoreType=image/gif&amp;s=24'
alt='periodic in x with period 2 π'
title='periodic in x with period 2 π'
width='184'
height='20'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>periodic in x with period 2 π</plaintext>
</subpod>
<subpod title='Parity'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488623h005d7ihcg97g200002a927651b87b97f0?MSPStoreType=image/gif&amp;s=24'
alt='odd'
title='odd'
width='24'
height='18'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>odd</plaintext>
</subpod>
<expressiontypes count='4'>
<expressiontype name='Default' />
<expressiontype name='Default' />
<expressiontype name='Default' />
<expressiontype name='Default' />
</expressiontypes>
<states count='1'>
<state name='Approximate forms'
input='PropertiesAsARealFunction__Approximate forms' />
</states>
<infos count='1'>
<info text='R is the set of real numbers'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488723h005d7ihcg97g200004ecf386f45a96ie7?MSPStoreType=image/gif&amp;s=24'
alt='R is the set of real numbers'
title='R is the set of real numbers'
width='179'
height='18' />
<link url='http://reference.wolfram.com/language/ref/Reals.html'
text='Documentation'
title='Documentation' />
<link url='http://mathworld.wolfram.com/R.html'
text='Definition'
title='MathWorld' />
</info>
</infos>
</pod>
<pod title='Series expansion at x = 0'
scanner='Series'
id='SeriesExpansionAt `1`x=0.'
position='600'
error='false'
numsubpods='1'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488823h005d7ihcg97g20000397b8319ei591b6b?MSPStoreType=image/gif&amp;s=24'
alt='x - x^3/6 + x^5/120 + O(x^6)
(Taylor series)'
title='x - x^3/6 + x^5/120 + O(x^6)
(Taylor series)'
width='132'
height='58'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>x - x^3/6 + x^5/120 + O(x^6)
(Taylor series)</plaintext>
</subpod>
<expressiontypes count='1'>
<expressiontype name='Default' />
</expressiontypes>
<infos count='1'>
<info>
<link url='http://mathworld.wolfram.com/Big-ONotation.html'
text='Big‐O notation' />
</info>
</infos>
</pod>
<pod title='Derivative'
scanner='Derivative'
id='Derivative'
position='700'
error='false'
numsubpods='1'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP488923h005d7ihcg97g20000408129777bei9ef4?MSPStoreType=image/gif&amp;s=24'
alt='d/dx(sin(x)) = cos(x)'
title='d/dx(sin(x)) = cos(x)'
width='119'
height='36'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>d/dx(sin(x)) = cos(x)</plaintext>
</subpod>
<expressiontypes count='1'>
<expressiontype name='Default' />
</expressiontypes>
<states count='1'>
<state name='Step-by-step solution'
input='Derivative__Step-by-step solution'
stepbystep='true' />
</states>
</pod>
<pod title='Indefinite integral'
scanner='Integral'
id='IndefiniteIntegral'
position='800'
error='false'
numsubpods='1'
primary='true'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489023h005d7ihcg97g200003hae4i65ga7g839f?MSPStoreType=image/gif&amp;s=24'
alt='integral sin(x) dx = -cos(x) + constant'
title='integral sin(x) dx = -cos(x) + constant'
width='209'
height='32'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>integral sin(x) dx = -cos(x) + constant</plaintext>
</subpod>
<expressiontypes count='1'>
<expressiontype name='Default' />
</expressiontypes>
<states count='1'>
<state name='Step-by-step solution'
input='IndefiniteIntegral__Step-by-step solution'
stepbystep='true' />
</states>
</pod>
<pod title='Identities'
scanner='FunctionProperties'
id='Identities'
position='900'
error='false'
numsubpods='8'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489123h005d7ihcg97g2000037e5c2i7e1eb218c?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = -i sinh(π - i x)'
title='sin(x) = -i sinh(π - i x)'
width='141'
height='18'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = -i sinh(π - i x)</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489223h005d7ihcg97g2000051c69iac0cig2h67?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = i sinh(π + i x)'
title='sin(x) = i sinh(π + i x)'
width='132'
height='18'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = i sinh(π + i x)</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489323h005d7ihcg97g2000051e9icih860a8204?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = i sinh(2 π - i x)'
title='sin(x) = i sinh(2 π - i x)'
width='143'
height='18'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = i sinh(2 π - i x)</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489423h005d7ihcg97g200002ag65be223e852a7?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = -i sinh(2 π + i x)'
title='sin(x) = -i sinh(2 π + i x)'
width='152'
height='18'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = -i sinh(2 π + i x)</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489523h005d7ihcg97g20000536g46egbhag9e35?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = 3 sin(x/3) - 4 sin^3(x/3)'
title='sin(x) = 3 sin(x/3) - 4 sin^3(x/3)'
width='179'
height='33'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = 3 sin(x/3) - 4 sin^3(x/3)</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489623h005d7ihcg97g200004hg847ffcf68b3g2?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = 2 cos(x/2) sin(x/2)'
title='sin(x) = 2 cos(x/2) sin(x/2)'
width='152'
height='33'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = 2 cos(x/2) sin(x/2)</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489723h005d7ihcg97g20000233cg868429319b4?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = i (-1)^m sinh(m π - i x) for m element Z'
title='sin(x) = i (-1)^m sinh(m π - i x) for m element Z'
width='255'
height='18'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = i (-1)^m sinh(m π - i x) for m element Z</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489823h005d7ihcg97g200004heg6g38hc4i2e52?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = 1/2 sec(b) (-sin(b - x) + sin(b + x))'
title='sin(x) = 1/2 sec(b) (-sin(b - x) + sin(b + x))'
width='253'
height='36'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = 1/2 sec(b) (-sin(b - x) + sin(b + x))</plaintext>
</subpod>
<expressiontypes count='8'>
<expressiontype name='Default' />
<expressiontype name='Default' />
<expressiontype name='Default' />
<expressiontype name='Default' />
<expressiontype name='Default' />
<expressiontype name='Default' />
<expressiontype name='Default' />
<expressiontype name='Default' />
</expressiontypes>
<infos count='2'>
<info text='sinh(x) is the hyperbolic sine function'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP489923h005d7ihcg97g20000425aaide8fb495ig?MSPStoreType=image/gif&amp;s=24'
alt='sinh(x) is the hyperbolic sine function'
title='sinh(x) is the hyperbolic sine function'
width='244'
height='18' />
<link url='http://reference.wolfram.com/language/ref/Sinh.html'
text='Documentation'
title='Mathematica' />
<link url='http://functions.wolfram.com/ElementaryFunctions/Sinh'
text='Properties'
title='Wolfram Functions Site' />
<link url='http://mathworld.wolfram.com/HyperbolicSine.html'
text='Definition'
title='MathWorld' />
</info>
<info text='sec(x) is the secant function'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490023h005d7ihcg97g2000014i56f97f2b2dhei?MSPStoreType=image/gif&amp;s=24'
alt='sec(x) is the secant function'
title='sec(x) is the secant function'
width='180'
height='18' />
<link url='http://reference.wolfram.com/language/ref/Sec.html'
text='Documentation'
title='Mathematica' />
<link url='http://functions.wolfram.com/ElementaryFunctions/Sec'
text='Properties'
title='Wolfram Functions Site' />
<link url='http://mathworld.wolfram.com/Secant.html'
text='Definition'
title='MathWorld' />
</info>
</infos>
</pod>
<pod title='Global maxima'
scanner='GlobalExtrema'
id='GlobalMaximum'
position='1000'
error='false'
numsubpods='1'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490123h005d7ihcg97g20000113f6a563d635a1h?MSPStoreType=image/gif&amp;s=24'
alt='max{sin(x)} = 1 at x = 2 π n + π/2 for integer n'
title='max{sin(x)} = 1 at x = 2 π n + π/2 for integer n'
width='296'
height='32'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>max{sin(x)} = 1 at x = 2 π n + π/2 for integer n</plaintext>
</subpod>
<expressiontypes count='1'>
<expressiontype name='Default' />
</expressiontypes>
<states count='2'>
<state name='Approximate form'
input='GlobalMaximum__Approximate form' />
<state name='Step-by-step solution'
input='GlobalMaximum__Step-by-step solution'
stepbystep='true' />
</states>
</pod>
<pod title='Global minima'
scanner='GlobalExtrema'
id='GlobalMinimum'
position='1100'
error='false'
numsubpods='2'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490223h005d7ihcg97g200001h39d0g28ib6b914?MSPStoreType=image/gif&amp;s=24'
alt='min{sin(x)} = -1 at x = 2 π n - π/2 for integer n'
title='min{sin(x)} = -1 at x = 2 π n - π/2 for integer n'
width='302'
height='32'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>min{sin(x)} = -1 at x = 2 π n - π/2 for integer n</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490323h005d7ihcg97g2000029i28c1ahcd696a7?MSPStoreType=image/gif&amp;s=24'
alt='min{sin(x)} = -1 at x = 2 π n + (3 π)/2 for integer n'
title='min{sin(x)} = -1 at x = 2 π n + (3 π)/2 for integer n'
width='312'
height='36'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>min{sin(x)} = -1 at x = 2 π n + (3 π)/2 for integer n</plaintext>
</subpod>
<expressiontypes count='2'>
<expressiontype name='Default' />
<expressiontype name='Default' />
</expressiontypes>
<states count='2'>
<state name='Approximate forms'
input='GlobalMinimum__Approximate forms' />
<state name='Step-by-step solution'
input='GlobalMinimum__Step-by-step solution'
stepbystep='true' />
</states>
</pod>
<pod title='Alternative representations'
scanner='MathematicalFunctionData'
id='AlternativeRepresentations:MathematicalFunctionIdentityData'
position='1200'
error='false'
numsubpods='3'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490423h005d7ihcg97g200000h121iie41i1758g?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = 1/csc(x)'
title='sin(x) = 1/csc(x)'
width='94'
height='46'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = 1/csc(x)</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490523h005d7ihcg97g200005b65eife3i0fc50a?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = cos(π/2 - x)'
title='sin(x) = cos(π/2 - x)'
width='119'
height='39'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = cos(π/2 - x)</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490623h005d7ihcg97g200000hei26fce8855hf4?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = -cos(π/2 + x)'
title='sin(x) = -cos(π/2 + x)'
width='128'
height='39'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = -cos(π/2 + x)</plaintext>
</subpod>
<expressiontypes count='3'>
<expressiontype name='Default' />
<expressiontype name='Default' />
<expressiontype name='Default' />
</expressiontypes>
<states count='1'>
<state name='More'
input='AlternativeRepresentations:MathematicalFunctionIdentityData__More' />
</states>
<infos count='2'>
<info text='csc(x) is the cosecant function'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490723h005d7ihcg97g200005c2ci581e0410i30?MSPStoreType=image/gif&amp;s=24'
alt='csc(x) is the cosecant function'
title='csc(x) is the cosecant function'
width='195'
height='18' />
<link url='http://reference.wolfram.com/language/ref/Csc.html'
text='Documentation'
title='Mathematica' />
<link url='http://functions.wolfram.com/ElementaryFunctions/Csc'
text='Properties'
title='Wolfram Functions Site' />
<link url='http://mathworld.wolfram.com/Cosecant.html'
text='Definition'
title='MathWorld' />
</info>
<info>
<link url='http://functions.wolfram.com/ElementaryFunctions/Sin/27/ShowAll.html'
text='More information' />
</info>
</infos>
</pod>
<pod title='Series representations'
scanner='MathematicalFunctionData'
id='SeriesRepresentations:MathematicalFunctionIdentityData'
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<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490823h005d7ihcg97g20000223d2ba6ch9cg993?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = sum_(k=0)^∞ ((-1)^k x^(1 + 2 k))/((1 + 2 k)!)'
title='sin(x) = sum_(k=0)^∞ ((-1)^k x^(1 + 2 k))/((1 + 2 k)!)'
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<plaintext>sin(x) = sum_(k=0)^∞ ((-1)^k x^(1 + 2 k))/((1 + 2 k)!)</plaintext>
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<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP490923h005d7ihcg97g20000333518hfbeief76d?MSPStoreType=image/gif&amp;s=24'
alt='sin(x)∝( sum_(k=0)^∞ (-1)^k (d^(2 k) δ(x))/(dx^(2 k)))/θ(x)'
title='sin(x)∝( sum_(k=0)^∞ (-1)^k (d^(2 k) δ(x))/(dx^(2 k)))/θ(x)'
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<plaintext>sin(x)∝( sum_(k=0)^∞ (-1)^k (d^(2 k) δ(x))/(dx^(2 k)))/θ(x)</plaintext>
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<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491023h005d7ihcg97g200002fh72048bh406344?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = 2 sum_(k=0)^∞ (-1)^k J_(1 + 2 k)(x)'
title='sin(x) = 2 sum_(k=0)^∞ (-1)^k J_(1 + 2 k)(x)'
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colorinvertable='true' />
<plaintext>sin(x) = 2 sum_(k=0)^∞ (-1)^k J_(1 + 2 k)(x)</plaintext>
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<expressiontype name='Default' />
<expressiontype name='Default' />
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<info text='n! is the factorial function'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491123h005d7ihcg97g200004c0f017be19b7f0c?MSPStoreType=image/gif&amp;s=24'
alt='n! is the factorial function'
title='n! is the factorial function'
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height='18' />
<link url='http://reference.wolfram.com/language/ref/Factorial.html'
text='Documentation'
title='Mathematica' />
<link url='http://functions.wolfram.com/GammaBetaErf/Factorial'
text='Properties'
title='Wolfram Functions Site' />
<link url='http://mathworld.wolfram.com/Factorial.html'
text='Definition'
title='MathWorld' />
</info>
<info text='θ(x) is the Heaviside step function'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491223h005d7ihcg97g2000010c59697b2a111h4?MSPStoreType=image/gif&amp;s=24'
alt='θ(x) is the Heaviside step function'
title='θ(x) is the Heaviside step function'
width='216'
height='18' />
<link url='http://reference.wolfram.com/language/ref/HeavisideTheta.html'
text='Documentation'
title='Mathematica' />
<link url='http://functions.wolfram.com/GeneralizedFunctions/UnitStep'
text='Properties'
title='Wolfram Functions Site' />
<link url='http://mathworld.wolfram.com/HeavisideStepFunction.html'
text='Definition'
title='MathWorld' />
</info>
<info text='δ(x) is the Dirac delta function'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491323h005d7ihcg97g200002e85433e829ie851?MSPStoreType=image/gif&amp;s=24'
alt='δ(x) is the Dirac delta function'
title='δ(x) is the Dirac delta function'
width='195'
height='18' />
<link url='http://reference.wolfram.com/language/ref/DiracDelta.html'
text='Documentation'
title='Mathematica' />
<link url='http://functions.wolfram.com/GeneralizedFunctions/DiracDelta'
text='Properties'
title='Wolfram Functions Site' />
<link url='http://mathworld.wolfram.com/DeltaFunction.html'
text='Definition'
title='MathWorld' />
</info>
<info text='J_n(z) is the Bessel function of the first kind'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491423h005d7ihcg97g200002e2e43553cff291h?MSPStoreType=image/gif&amp;s=24'
alt='J_n(z) is the Bessel function of the first kind'
title='J_n(z) is the Bessel function of the first kind'
width='278'
height='18' />
<link url='http://reference.wolfram.com/language/ref/BesselJ.html'
text='Documentation'
title='Mathematica' />
<link url='http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ'
text='Properties'
title='Wolfram Functions Site' />
<link url='http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html'
text='Definition'
title='MathWorld' />
</info>
<info>
<link url='http://functions.wolfram.com/ElementaryFunctions/Sin/06/ShowAll.html'
text='More information' />
</info>
</infos>
</pod>
<pod title='Integral representations'
scanner='MathematicalFunctionData'
id='IntegralRepresentations:MathematicalFunctionIdentityData'
position='1400'
error='false'
numsubpods='3'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491523h005d7ihcg97g2000037i4feh0a12ai85g?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = x integral_0^1 cos(t x) dt'
title='sin(x) = x integral_0^1 cos(t x) dt'
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<plaintext>sin(x) = x integral_0^1 cos(t x) dt</plaintext>
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<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491623h005d7ihcg97g200003bh805d217ca2213?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = -(i x)/(4 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) e^(s - x^2/(4 s))/s^(3/2) ds for γ&gt;0'
title='sin(x) = -(i x)/(4 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) e^(s - x^2/(4 s))/s^(3/2) ds for γ&gt;0'
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height='55'
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themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>sin(x) = -(i x)/(4 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) e^(s - x^2/(4 s))/s^(3/2) ds for γ&gt;0</plaintext>
</subpod>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491723h005d7ihcg97g200000d65b6198f68gfa2?MSPStoreType=image/gif&amp;s=24'
alt='sin(x) = -i/(2 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) (2^(-1 + 2 s) x^(1 - 2 s) Γ(s))/Γ(3/2 - s) ds for (0&lt;γ&lt;1 and x&gt;0)'
title='sin(x) = -i/(2 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) (2^(-1 + 2 s) x^(1 - 2 s) Γ(s))/Γ(3/2 - s) ds for (0&lt;γ&lt;1 and x&gt;0)'
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themes='1,2,3,4,5,6,7,8,9,10,11,12'
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<plaintext>sin(x) = -i/(2 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) (2^(-1 + 2 s) x^(1 - 2 s) Γ(s))/Γ(3/2 - s) ds for (0&lt;γ&lt;1 and x&gt;0)</plaintext>
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<expressiontypes count='3'>
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<expressiontype name='Default' />
<expressiontype name='Default' />
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<infos count='2'>
<info text='Γ(x) is the gamma function'>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491823h005d7ihcg97g200004dh85520h4d848d8?MSPStoreType=image/gif&amp;s=24'
alt='Γ(x) is the gamma function'
title='Γ(x) is the gamma function'
width='176'
height='18' />
<link url='http://reference.wolfram.com/language/ref/Gamma.html'
text='Documentation'
title='Mathematica' />
<link url='http://functions.wolfram.com/GammaBetaErf/Gamma'
text='Properties'
title='Wolfram Functions Site' />
<link url='http://mathworld.wolfram.com/GammaFunction.html'
text='Definition'
title='MathWorld' />
</info>
<info>
<link url='http://functions.wolfram.com/ElementaryFunctions/Sin/07/ShowAll.html'
text='More information' />
</info>
</infos>
</pod>
<pod title='Definite integral over a half-period'
scanner='InterestingDefiniteIntegrals'
id='DefiniteIntegralOverAHalfPeriod'
position='1500'
error='false'
numsubpods='1'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP491923h005d7ihcg97g20000214fi1a3fic6gg59?MSPStoreType=image/gif&amp;s=24'
alt='integral_0^π sin(x) dx = 2'
title='integral_0^π sin(x) dx = 2'
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height='33'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>integral_0^π sin(x) dx = 2</plaintext>
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<expressiontypes count='1'>
<expressiontype name='Default' />
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<pod title='Definite integral mean square'
scanner='InterestingDefiniteIntegrals'
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position='1600'
error='false'
numsubpods='1'>
<subpod title=''>
<img src='https://www5a.wolframalpha.com/Calculate/MSP/MSP492023h005d7ihcg97g200002bb00a8600a3i444?MSPStoreType=image/gif&amp;s=24'
alt='integral_0^(2 π) (sin^2(x))/(2 π) dx = 1/2 = 0.5'
title='integral_0^(2 π) (sin^2(x))/(2 π) dx = 1/2 = 0.5'
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height='39'
type='Default'
themes='1,2,3,4,5,6,7,8,9,10,11,12'
colorinvertable='true' />
<plaintext>integral_0^(2 π) (sin^2(x))/(2 π) dx = 1/2 = 0.5</plaintext>
</subpod>
<expressiontypes count='1'>
<expressiontype name='Default' />
</expressiontypes>
</pod>
</queryresult>
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