Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bqv8)

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=-13/8, b>=a

For fixed z and a=-13/8, b=47/8

http://functions.wolfram.com/07.23.03.bqv8.01

Input Form

Hypergeometric2F1[-(13/8), 47/8, -(21/4), z] == (1/(16290624 2^(1/4) (-1 + z)^9)) ((1 + Sqrt[1 - z])^(1/4) (-8145312 + 57986864 z - 163962906 z^2 + 211539257 z^3 - 64843072 z^4 - 91185570 z^5 + 340298818 z^6 - 386144367 z^7 + 226898784 z^8 - 70312704 z^9 + 9146368 z^10 + (1/Sqrt[1 - z]) (2 (-4072656 + 31029760 z - 95969087 z^2 + 143390717 z^3 - 76711670 z^4 - 38500574 z^5 - 601761107 z^6 + 1179436641 z^7 - 1073462376 z^8 + 548976960 z^9 - 153201664 z^10 + 18292736 z^11))))

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]