Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c69s)

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=17/8, b>=a

For fixed z and a=17/8, b=23/8

http://functions.wolfram.com/07.23.03.c69s.01

Input Form

Hypergeometric2F1[17/8, 23/8, -(11/2), z] == (1/(2838528 (1 - z)^(21/2))) (Sqrt[1 - z] (2838528 - 31627008 z + 164462816 z^2 - 537859443 z^3 + 1286214883 z^4 - 2669173646 z^5 + 8371504566 z^6 + 5386517169 z^7 + 135291351 z^8) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (709632 - 8128512 z + 43492316 z^2 - 146318323 z^3 + 358688267 z^4 - 752717534 z^5 + 37141466610 z^6 + 11660193057 z^7 + 135291351 z^8) Sin[ArcSin[Sqrt[z]]/4])

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]