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

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=-29/8, b>=a

For fixed z and a=-29/8, b=47/8

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

Input Form

Hypergeometric2F1[-(29/8), 47/8, -(9/2), -z] == (1/(6571008 (1 + z)^(51/8))) (2 (3285504 + 4471936 z - 3606354 z^2 + 4173189 z^3 - 7008790 z^4 + 34444317 z^5 + 371987802 z^6 + 822045312 z^7 + 813998592 z^8 + 389283840 z^9 + 73531392 z^10) Cos[(3 ArcTan[Sqrt[z]])/4] - Sqrt[z] (-4928256 - 5989200 z + 6118253 z^2 - 7274739 z^3 + 11826531 z^4 + 430199763 z^5 + 1083788640 z^6 + 1141873920 z^7 + 567840768 z^8 + 110297088 z^9) 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]