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

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=-39/8, b>=a

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

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, -(7/2), -z] == (1/(1922816 (1 + z)^(33/8))) ((1922816 - 7193392 z + 27862591 z^2 - 147106154 z^3 + 1930025487 z^4 + 21515956176 z^5 + 62002347264 z^6 + 79330099200 z^7 + 47905701888 z^8 + 11176771584 z^9) Cos[ArcTan[Sqrt[z]]/4] - 4 Sqrt[z] (-120176 + 487142 z - 1903502 z^2 + 9834045 z^3 + 718373799 z^4 + 2776927296 z^5 + 4147993344 z^6 + 2775810048 z^7 + 698548224 z^8) 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]