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

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=17/4

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

Input Form

Hypergeometric2F1[-(17/4), 17/4, 4, z] == (1/(50470875 Pi Sqrt[1 + Sqrt[z]] z^3)) (256 ((-544 - 544 Sqrt[z] - 2567 z - 2567 z^(3/2) - 17850 z^2 - 17850 z^(5/2) + 933545 z^3 + 933545 z^(7/2) - 3563000 z^4 - 3563000 z^(9/2) + 5296368 z^5 + 5296368 z^(11/2) - 3533376 z^6 - 3533376 z^(13/2) + 887040 z^7 + 887040 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (-544 - 2431 z - 17170 z^2 + 543905 z^3 - 1940560 z^4 + 2776928 z^5 - 1803648 z^6 + 443520 z^7) 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]