Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b963)

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=-41/8, b>=a

For fixed z and a=-41/8, b=19/8

http://functions.wolfram.com/07.23.03.b963.01

Input Form

Hypergeometric2F1[-(41/8), 19/8, -(17/4), z] == (-7072 - 11856 z - 20282 z^2 - 39263 z^3 - 102816 z^4 - 926464 z^5 + 1118208 z^6 - (1/Sqrt[1 - z]) (2 (3536 + 4160 z + 6735 z^2 + 13599 z^3 + 39816 z^4 + 434112 z^5 - 1254400 z^6 + 745472 z^7)))/ (7072 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + z))

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]