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

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=-17/4, b>=a

For fixed z and a=-17/4, b=5/4

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

Input Form

Hypergeometric2F1[-(17/4), 5/4, 3, z] == (1/(1044225 Pi Sqrt[1 + Sqrt[z]] z^2)) (64 (2 (1326 + 1326 Sqrt[z] - 5967 z - 5967 z^(3/2) + 32775 z^2 + 32775 z^(5/2) - 51065 z^3 - 51065 z^(7/2) + 41475 z^4 + 41475 z^(9/2) - 17472 z^5 - 17472 z^(11/2) + 3024 z^6 + 3024 z^(13/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (2652 - 12597 z + 35715 z^2 - 53875 z^3 + 42805 z^4 - 17724 z^5 + 3024 z^6) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

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]