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

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=-7/8, b>=a

For fixed z and a=-7/8, b=45/8

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

Input Form

Hypergeometric2F1[-(7/8), 45/8, -(19/4), z] == (1/(93290912 2^(3/4) (-1 + z)^9)) ((1 + Sqrt[1 - z])^(3/4) (-46645456 + 362729796 z - 1173348033 z^2 + 1922506976 z^3 - 1253150262 z^4 + 3960127488 z^5 - 3873330433 z^6 + 2051891364 z^7 - 589200384 z^8 + 72281088 z^9 + (1/Sqrt[1 - z]) (-46645456 + 386052524 z - 1348882249 z^2 + 2466755109 z^3 - 2088583770 z^4 - 6048711258 z^5 + 9612844963 z^6 - 7476768263 z^7 + 3403668064 z^8 - 867920640 z^9 + 96374784 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]