Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2sp)

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=9/8, b>=a

For fixed z and a=9/8, b=45/8

http://functions.wolfram.com/07.23.03.c2sp.01

Input Form

Hypergeometric2F1[9/8, 45/8, -(7/4), z] == (1/(390572 2^(3/4) (-1 + z)^8)) ((1 + Sqrt[1 - z])^(3/4) (2 (97643 - 1115920 z - 150356278 z^2 - 9224012 z^3 + 3083587 z^4 - 708860 z^5 + 77280 z^6) + (1/Sqrt[1 - z]) (195286 - 2329483 z + 336477792 z^2 + 110971734 z^3 - 31561566 z^4 + 9830637 z^5 - 2066320 z^6 + 206080 z^7)))

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]