Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4ol)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-47/8, b>=a

For fixed z and a=-47/8, b=-35/8

http://functions.wolfram.com/07.23.03.b4ol.01

Input Form

Hypergeometric2F1[-(47/8), -(35/8), 9/4, z] == (1/(235582515 z^2)) (2 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-201066 + 32271093 z + 632155716 z^2 + 2380234703 z^3 + 2600794230 z^4 + 851571315 z^5 + 63210320 z^6 - 144855 z^7 - (1/Sqrt[1 - z]) (2 (-100533 + 16185813 z + 278574837 z^2 + 702869825 z^3 - 77710657 z^4 - 695821105 z^5 - 215934585 z^6 - 8160165 z^7 + 96570 z^8))))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]