Jcd Jcd_sub Jcn Jcn_sub Jcs Jcs_sub Jdc Jdc_sub Jdn Jdn_sub Jds Jds_sub Jelli Jnc Jnc_sub Jnd Jnd_sub Jns Jns_sub Jsc Jsc_sub Jsd Jsd_sub Jsn Jsn_sub Jtheta1 Jtheta1_sub Jtheta1t Jtheta1t_sub Jtheta2 Jtheta2_sub Jtheta2t Jtheta2t_sub Jtheta3 Jtheta3_sub Jtheta3m1 Jtheta3m1_sub Jtheta3m1t Jtheta3m1t_sub Jtheta3t Jtheta3t_sub Jtheta4 Jtheta4_sub Jtheta4m1 Jtheta4m1_sub Jtheta4m1t Jtheta4m1t_sub Jtheta4t Jtheta4t_sub

Jtheta3m1t_sub() Sub Jtheta3m1t_sub ( Ret As  Double, X As  Double, Tau As  Double, Optional Info As  Long  ) Jacobi theta function θ3(x, τ) - 1 (Subroutine version) Purpose Computes the Jacobi theta function θ3 - 1. θ3(x, τ) = 2Σ(-1)^n exp(iπτ)^(n + 1/2) sin((2n + 1)x) (Σ for n = 0 to ∞) Parameters [out] Ret Jacobi theta function θ3(x, τ) - 1. [in] X Argument x. [in] Tau Assuming that the argument τ is a purely imaginary number, it is expressed as a real number (τ = i*Tau). This is equivalent to setting q = exp(iπτ) in θ3(x, q). [out] Info (Optional) = 0: Successful exit. = 1: Floating point range error. Reference boost/math/special_functions