WJcd WJcn WJcs WJdc WJdn WJds WJnc WJnd WJsc WJsd WJsn WJtheta1 WJtheta1t WJtheta2 WJtheta2t WJtheta3 WJtheta3m1 WJtheta3m1t WJtheta3t WJtheta4 WJtheta4m1 WJtheta4m1t WJtheta4t

WJtheta1t() Function WJtheta1t ( X As  Double, Q As  Double  ) Jacobi theta function θ1(x, τ) Purpose This function computes the Jacobi theta function θ1. θ1(x, τ) = 2Σ(-1)^n exp(iπτ)^(n + 1/2) sin((2n + 1)x) (Σ for n = 0 to ∞) Returns Jacobi theta function θ1(x, τ). Parameters [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 θ1(x, q). Reference boost/math/special_functions