Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2un)

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=47/8

http://functions.wolfram.com/07.23.03.c2un.01

Input Form

Hypergeometric2F1[9/8, 47/8, -(7/2), z] == (1/(1277696 (1 - z)^(21/2))) (Sqrt[1 - z] (1277696 - 15229680 z + 89135695 z^2 - 373574211 z^3 + 1977116202 z^4 + 1388421226 z^5 - 347185245 z^6 + 88442025 z^7 - 15532748 z^8 + 1321936 z^9) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (319424 - 3907240 z + 23431319 z^2 - 99876327 z^3 + 10013302562 z^4 + 1551877754 z^5 - 389547285 z^6 + 96043157 z^7 - 16193716 z^8 + 1321936 z^9) 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]