get_u_reg_expr()

gistfile1.py

def get_u_reg_expr():
    '''
    SymPy expression for expected solution to the regularized problem.
    '''
    k, R, r, th = symbols('k R r th')
    
    a = pi/6
    nu = pi / (2*pi - a)
    
    # True solution to original problem
    u = besselj(nu/2, k*r) * sin(nu*(th-a)/2)
    
    # Inhomogeneous part of asymptotic expansion
    u -= get_u_asympt_expr()
    
    # Compute the shc_coef using quadratures
    problem = ShcBesselKnown()  
    
    # Homogeneous part of asymptotic expansion  
    for m in range(1, len(problem.shc_coef)+1):
        u -= problem.shc_coef[m-1] * besselj(m*nu, k*r) * sin(m*nu*(th - a))
        
    return u