Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.acl3)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-13/4, b>=a

For fixed z and a=-13/4, b=9/4

http://functions.wolfram.com/07.23.03.acl3.01

Input Form

Hypergeometric2F1[-(13/4), 9/4, 9/2, -z] == (1/(14421 z^(7/2) Sqrt[-1 + Sqrt[1 + z]])) (8 Sqrt[2] ((104 + 416 z + 377 z^2 - 325 z^3 - 1113 z^4 - 1199 z^5 - 588 z^6 - 112 z^7)/Sqrt[1 + z] + 2 (-52 - 182 z - 104 z^2 + 195 z^3 + 906 z^4 + 1073 z^5 + 560 z^6 + 112 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]