XLPack 6.1
C/C++ API Reference Manual
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◆ _hyp2f1()

double _hyp2f1 ( double  a1,
double  a2,
double  b,
double  z 
)

Hypergeometric function 2F1(a1, a2; b; z) (Gaussian hypergeometric function)

Purpose
hyp2f1 computes the hypergeometric function 2F1(a1, a2; b; z).
2F1(a1, a2; b; z) = Σ(a1)k*(a2)k/(b)k * z^k/k! (k = 1 to ∞)
Returns
2F1(a1, a2; b; z).
Parameters
[in]a1Argument a1.
[in]a2Argument a2.
[in]bArgument b.
[in]zArgument z.
Error handling
  • If z is outside the addressed range, domain error (EDOM) occurs.
  • Range error (ERANGE) may occur.
Notes
  • z < -1 and z > 1 are not addressed except for some special cases.
  • The parameters a1, a2 and b ranging from -1 to 7 are tested (-7 to 7 for some special cases). It is recommended to use within this range.
  • The parameters a1, a2 and b are considered to be integer valued if they are within 1.0e-13 of the nearest integer.
Reference
netlib/cephes