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

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=-21/8, b>=a

For fixed z and a=-21/8, b=15/8

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

Input Form

Hypergeometric2F1[-(21/8), 15/8, 23/4, z] == (1/(8927703 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-34320 + 196196 z - 433121 z^2 + 400387 z^3 + 52325 z^4 - 78499 z^5 + 39560 z^6 - 7360 z^7 + (1/Sqrt[1 - z]) (34320 - 213356 z + 526929 z^2 - 594568 z^3 + 104650 z^4 + 413356 z^5 - 420371 z^6 + 178480 z^7 - 29440 z^8)))

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]