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

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.basw.01

Input Form

Hypergeometric2F1[-(39/8), 45/8, 11/2, z] == (1/(9720340053765 z^(9/2))) (512 ((1 + Sqrt[z])^(19/4) (1277696 - 6069056 Sqrt[z] + 21298736 z - 57547656 z^(3/2) + 142348311 z^2 - 316512108 z^(5/2) + 702858288 z^3 - 1487785728 z^(7/2) + 3836921088 z^4 - 167574528 z^(9/2) - 33736310784 z^5 + 88017076224 z^(11/2) - 98862956544 z^6 + 53089665024 z^(13/2) - 11176771584 z^7) + (1 - Sqrt[z])^(19/4) (-1277696 - 6069056 Sqrt[z] - 21298736 z - 57547656 z^(3/2) - 142348311 z^2 - 316512108 z^(5/2) - 702858288 z^3 - 1487785728 z^(7/2) - 3836921088 z^4 - 167574528 z^(9/2) + 33736310784 z^5 + 88017076224 z^(11/2) + 98862956544 z^6 + 53089665024 z^(13/2) + 11176771584 z^7)))

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]