XLPack 7.0
XLPack Numerical Library (C API) Reference Manual
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◆ celli1()

double celli1 ( double  k)

Complete elliptic integral of the first kind K(k)

Purpose
celli1 computes the Legendre form of complete elliptic integral of the first kind K(k).
K(k) = F(π/2, k)
where F(φ, k) is the incomplete elliptic integral of the first kind defined as follows:
F(φ, k) = ∫ 1/sqrt(1 - k^2(sin(t))^2) dt [0, φ]
Returns
Complete elliptic integral of the first kind K(k).
Parameters
[in]kArgument k. (|k| < 1)
Error handling
  • If |k| > 1, domain error (EDOM) occurs.
  • Range error (ERANGE) may occur.
Reference
boost/math/special_functions