Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.abs1)

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=19/4

http://functions.wolfram.com/07.23.03.abs1.01

Input Form

Hypergeometric2F1[-(15/4), 19/4, 5, z] == (1/(140821065 Pi Sqrt[1 + Sqrt[z]] z^4)) (4096 (-8 (16 + 16 Sqrt[z] + 34 z + 34 z^(3/2) + 99 z^2 + 99 z^(5/2) + 504 z^3 + 504 z^(7/2) - 6315 z^4 - 6315 z^(9/2) + 13446 z^5 + 13446 z^(11/2) - 10920 z^6 - 10920 z^(13/2) + 3120 z^7 + 3120 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (128 + 240 z + 715 z^2 + 3810 z^3 + 17163 z^4 - 137976 z^5 + 253200 z^6 - 187200 z^7 + 49920 z^8) 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]