Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b761)

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=-45/8, b>=a

For fixed z and a=-45/8, b=39/8

http://functions.wolfram.com/07.23.03.b761.01

Input Form

Hypergeometric2F1[-(45/8), 39/8, -(5/2), -z] == (1/(45632 (1 + z)^(11/8))) ((-(-45632 + 450616 z - 3989235 z^2 + 70398768 z^3 + 1445613312 z^4 + 5222350848 z^5 + 6700728320 z^6 + 2848980992 z^7)) Cos[(3 ArcTan[Sqrt[z]])/4] + Sqrt[z] (34224 - 342953 z + 3043084 z^2 + 726815232 z^3 + 3300723712 z^4 + 4713938944 z^5 + 2136735744 z^6) Sin[(3 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]