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

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=-25/8, b>=a

For fixed z and a=-25/8, b=43/8

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

Input Form

Hypergeometric2F1[-(25/8), 43/8, -(11/2), z] == (1/5677056) ((1/(1 - Sqrt[z])^(31/4)) (2838528 - 21998592 Sqrt[z] + 82914048 z - 209486592 z^(3/2) + 408776928 z^2 - 662454996 z^(5/2) + 925772319 z^3 - 1135637136 z^(7/2) + 1226330784 z^4 - 1152176256 z^(9/2) + 912054528 z^5 - 571963392 z^(11/2) + 258306048 z^6 - 72630272 z^(13/2) + 9371648 z^7) + (1/(1 + Sqrt[z])^(31/4)) (2838528 + 21998592 Sqrt[z] + 82914048 z + 209486592 z^(3/2) + 408776928 z^2 + 662454996 z^(5/2) + 925772319 z^3 + 1135637136 z^(7/2) + 1226330784 z^4 + 1152176256 z^(9/2) + 912054528 z^5 + 571963392 z^(11/2) + 258306048 z^6 + 72630272 z^(13/2) + 9371648 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]