Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9094)

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=-23/4, b>=a

For fixed z and a=-23/4, b=-17/4

http://functions.wolfram.com/07.23.03.9094.01

Input Form

Hypergeometric2F1[-(23/4), -(17/4), 6, z] == (16384 Sqrt[1 + Sqrt[z]] ((15214592 - 375372512 z + 5001225087 z^2 - 52697819512 z^3 + 639635859940 z^4 + 29672591327736 z^5 + 93576203494074 z^6 + 82829382505656 z^7 + 22721048653284 z^8 + 1506334400040 z^9 + 302344575 z^10) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-15214592 + 15214592 Sqrt[z] + 363961568 z - 363961568 z^(3/2) - 4730036871 z^2 + 4730036871 z^(5/2) + 49192274995 z^3 - 49192274995 z^(7/2) - 603280302625 z^4 + 603280302625 z^(9/2) - 11714842303521 z^5 + 11714842303521 z^(11/2) - 26320098677691 z^6 + 26320098677691 z^(13/2) - 16283798160423 z^7 + 16283798160423 z^(15/2) - 2773682267355 z^8 + 2773682267355 z^(17/2) - 74074420875 z^9 + 74074420875 z^(19/2) + 604689150 z^10 - 604689150 z^(21/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/ (150770847054002175 Pi z^5)

Standard Form

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MathML Form

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</cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]