WAlaguerre WAlegendre WChebt WChebtd WChebu WGegenbauer WGegenbauerd WGegenbauerd1 WHermite WJacobi WJacobid WJacobid1 WJacobid2 WLaguerre WLegendre WLegendred WSharmonic WSharmonici WSharmonicr

WSharmonic() Function WSharmonic ( L As  Long, M As  Long, Theta As  Double, Phi As  Double  ) Spherical harmonic Ylm(θ, φ) Purpose This function computes the spherical harmonic of degree l, order m, polar angle θ and azimuth φ. Ylm(θ, φ) = [(2l + 1)/4π (l - m)!/(l + m)!]^(1/2) Plm(cosθ)exp(imφ), where m <= l. Plm(x) is an associated Legendre polynomial. Note that the phase factor of (-1)^m is included in Plm(x). Returns Spherical harmonic Ylm(θ, φ). Parameters [in] L Degree l. (0 <= L < 128) [in] M Order m. (|M| <= L) [in] Theta Polar angle θ. Generally use theta in the range [0, π]. For theta outside this range, the result may be different from the other implementation. [in] Phi Azimuth φ. Generally use phi in the range [0, 2π]. For phi outside this range, the result may be different from the other implementation. Reference boost/math/special_functions