Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9086)

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/07.23.03.9086.01

Input Form

Hypergeometric2F1[-(23/4), -(17/4), 4, z] == (1/(157941385977375 Pi z^3)) (256 Sqrt[1 + Sqrt[z]] ((33995104 - 1071908123 z + 25915955065 z^2 + 2125151998305 z^3 + 10034501438325 z^4 + 12393096311967 z^5 + 4518696973371 z^6 + 384224526555 z^7 + 106229175 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-33995104 + 33995104 Sqrt[z] + 1046411795 z - 1046411795 z^(3/2) - 25135130020 z^2 + 25135130020 z^(5/2) - 909965135415 z^3 + 909965135415 z^(7/2) - 3104293627050 z^4 + 3104293627050 z^(9/2) - 2697484800507 z^5 + 2697484800507 z^(11/2) - 613370456160 z^6 + 613370456160 z^(13/2) - 21139605825 z^7 + 21139605825 z^(15/2) + 212458350 z^8 - 212458350 z^(17/2)) 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]