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

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=-5/8, b>=a

For fixed z and a=-5/8, b=47/8

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

Input Form

Hypergeometric2F1[-(5/8), 47/8, -(21/4), z] == ((1 + Sqrt[1 - z])^(1/4) (2 (52944528 - 489106592 z + 1971544107 z^2 - 4448893979 z^3 + 5774458660 z^4 - 2924017278 z^5 + 4721057291 z^6 - 3549233991 z^7 + 1566809622 z^8 - 389370240 z^9 + 42301952 z^10) + (1/Sqrt[1 - z]) (105889056 - 1031157712 z + 4418958674 z^2 - 10753673483 z^3 + 15561927305 z^4 - 10721396686 z^5 - 47454339196 z^6 + 56375979033 z^7 - 36769185231 z^8 + 14648252640 z^9 - 3347622656 z^10 + 338415616 z^11)))/(211778112 2^(1/4) (-1 + z)^10)

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]