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

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=1/4

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

Input Form

Hypergeometric2F1[-(17/4), 1/4, 4, z] == (1/(777251475 Pi z^3)) (256 Sqrt[1 + Sqrt[z]] ((21216 - 207519 z + 1119144 z^2 + 6199270 z^3 - 2326940 z^4 + 898513 z^5 - 224532 z^6 + 25872 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-21216 + 21216 Sqrt[z] + 191607 z - 191607 z^(3/2) - 977925 z^2 + 977925 z^(5/2) - 838915 z^3 + 838915 z^(7/2) + 357665 z^4 - 357665 z^(9/2) - 100408 z^5 + 100408 z^(11/2) + 12936 z^6 - 12936 z^(13/2)) 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]