conatus.expert.Laguerre

class conatus.expert.Laguerre(coord, size, start=0.0, scale=1.0, dealias=REQUIRED)

Bases: Basis

Laguerre functions on the half line x >= start: f(x) = sum_n c_n L_n(y) exp(-y/2), y = (x - start)/scale (orthonormal). Functions decay like exp(-y/2); the wall x = start takes boundary conditions through tau terms written in the derivative bases L_n^(k)(y) exp(-y/2) (k = derivative level, the analogue of the ultraspherical index: d/dy and the conversion k -> k+1 are bidiagonal, multiplication by x tridiagonal). scale is the declared decay length (printed by explain()). Grid: Gauss-Laguerre nodes, floor(N * dealias) of them.

Parameters:

• coord (Coordinate)

• size (int)

• start (float)

• scale (float)

• dealias (Any)

family = 'Laguerre functions (half line)'

unbounded = True

coeff_space()

Return type:

str