Alaguerre Alaguerre_sub Alegendre Alegendre_sub Chebs Chebt Chebt_sub Chebtd Chebtd_sub Chebu Chebu_sub Gegenbauer Gegenbauer_sub Gegenbauerd Gegenbauerd1 Gegenbauerd1_sub Gegenbauerd_sub Hermite Hermite_sub Jacobi Jacobi_sub Jacobid Jacobid1 Jacobid1_sub Jacobid2 Jacobid2_sub Jacobid_sub Laguerre Laguerre_sub Legendre Legendre_sub Legendred Legendred_sub Sharmonic Sharmonici Sharmonici_sub Sharmonicr Sharmonicr_sub

Sharmonicr_sub() Sub Sharmonicr_sub ( Ret As  Double, L As  Long, M As  Long, Theta As  Double, Phi As  Double, Optional Info As  Long  ) Real part of spherical harmonic Ylm(θ, φ) (Subroutine version) Purpose Computes the real part of 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). Parameters [out] Ret Real part of spherical harmonic Ylm(θ, φ). [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. [out] Info (Optional) = 0: Successful exit. = -1: The argument L had an illegal value. (L < 0, L >= 128) = -2: The argument M had an illegal value. (|M| > L) = 1: Floating point range error. Reference boost/math/special_functions