XLPack 7.0
XLPack Numerical Library (C API) Reference Manual
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◆ hlambda()

double hlambda ( double  phi,
double  k 
)

Heuman lambda function Λ0(φ, k)

Purpose
This function computes the Heuman lambda function Λ0(φ, k).
Λ0(φ, k) = F(φ, √(1 - k^2))/K(√(1 - k^2)) + (2/π) K(k) Z(φ, √(1 - k^2))
where F is the incomplete elliptic integral of the first kind, K is the complete elliptic integral of the first kind, and Z is the Jacobi zeta function.
Returns
Heuman lambda function Λ0(φ, k).
Parameters
[in]phiArgument φ.
[in]kArgument k. (-1 <= k <= 1)
Error handling
  • If k < -1 or k > 1, domain error (EDOM) occurs.
  • Range error (ERANGE) may occur.
Reference
boost/math/special_functions