Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c6q6)

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=45/8

http://functions.wolfram.com/07.23.03.c6q6.01

Input Form

Hypergeometric2F1[17/8, 45/8, -(11/2), -z] == (1/(315392 (1 + z)^(105/8))) ((315392 + 4815104 z + 35524832 z^2 + 172004013 z^3 + 641423346 z^4 + 2204011615 z^5 + 11986092404 z^6 - 24303465573 z^7 + 4121124498 z^8 + 257272441 z^9 + 21130888 z^10 + 1034560 z^11) Cos[ArcTan[Sqrt[z]]/4] + Sqrt[z] (78848 + 1179136 z + 8519196 z^2 + 40432131 z^3 + 148371698 z^4 + 507622193 z^5 - 23891701144 z^6 + 14128203861 z^7 - 62713734 z^8 - 5201897 z^9 - 258640 z^10) Sin[ArcTan[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]