Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cc83)

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=33/8, b>=a

For fixed z and a=33/8, b=45/8

http://functions.wolfram.com/07.23.03.cc83.01

Input Form

Hypergeometric2F1[33/8, 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (-15004832 + 282808464 z - 2647917210 z^2 + 16847352191 z^3 - 86222006241 z^4 + 425298635307 z^5 + 78917273672055 z^6 + 136693167168285 z^7 + 54856232790957 z^8 + 4730576077161 z^9 + 1691668791 z^10 + (1/Sqrt[1 - z]) (2 (-7502416 + 145155440 z - 1393722919 z^2 + 9068448770 z^3 - 47165891044 z^4 + 233229288656 z^5 - 42611803829322 z^6 - 88903348579500 z^7 - 45992598999828 z^8 - 6269928272016 z^9 - 118980704967 z^10 + 1127779194 z^11))))/(30009664 2^(3/4) (-1 + z)^15)

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]