Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bcc7)

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=-37/8, b>=a

For fixed z and a=-37/8, b=47/8

http://functions.wolfram.com/07.23.03.bcc7.01

Input Form

Hypergeometric2F1[-(37/8), 47/8, -(13/4), z] == (1/(1334736 2^(1/4) (-1 + z)^4)) ((1 + Sqrt[1 - z])^(1/4) (4 (166842 + 737955 z + 3196379 z^2 + 19603935 z^3 - 798661479 z^4 + 2937722304 z^5 - 4276673280 z^6 + 2812575744 z^7 - 698548224 z^8) + (1/Sqrt[1 - z]) (667368 + 2618136 z + 11226185 z^2 + 71612294 z^3 + 7042105857 z^4 - 40987869648 z^5 + 90797507328 z^6 - 98448261120 z^7 + 52685242368 z^8 - 11176771584 z^9)))

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]