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

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=-35/8, b>=a

For fixed z and a=-35/8, b=-7/8

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

Input Form

Hypergeometric2F1[-(35/8), -(7/8), 21/4, z] == (16 2^(1/4) (124488 - 1685376 z + 11731797 z^2 - 64637601 z^3 + 2310574218 z^4 + 2153177918 z^5 - 7091975 z^6 + 832915 z^7 - 55760 z^8 + (1/Sqrt[1 - z]) (4 (-31122 + 436905 z - 3139731 z^2 + 17575152 z^3 + 181323438 z^4 - 123540727 z^5 - 79468455 z^6 + 7660030 z^7 - 871250 z^8 + 55760 z^9))))/(49069132305 (1 + Sqrt[1 - z])^(1/4) z^4)

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]