Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab7v)

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=-15/4, b>=a

For fixed z and a=-15/4, b=-5/4

http://functions.wolfram.com/07.23.03.ab7v.01

Input Form

Hypergeometric2F1[-(15/4), -(5/4), 5, z] == (1/(93364366095 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] ((-7040 + 94160 z - 667590 z^2 + 4146450 z^3 + 60590004 z^4 + 36387972 z^5 + 125970 z^6 - 6630 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (7040 - 7040 Sqrt[z] - 88880 z + 88880 z^(3/2) + 601755 z^2 - 601755 z^(5/2) - 3705240 z^3 + 3705240 z^(7/2) - 17714094 z^4 + 17714094 z^(9/2) - 4495140 z^5 + 4495140 z^(11/2) + 241995 z^6 - 241995 z^(13/2) - 13260 z^7 + 13260 z^(15/2)) 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]