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

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=15/4

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

Input Form

Hypergeometric2F1[-(17/4), 15/4, 5, -z] == (4096 Sqrt[2] (2 (42432 + 26520 z - 40443 z^2 + 147186 z^3 + 3106645 z^4 + 7995488 z^5 + 8759040 z^6 + 4538368 z^7 + 917504 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (42432 + 26520 z - 40443 z^2 + 147186 z^3 + 3106645 z^4 + 7995488 z^5 + 8759040 z^6 + 4538368 z^7 + 917504 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (84864 + 31824 z - 78897 z^2 + 311610 z^3 + 1953515 z^4 + 3019136 z^5 + 1939456 z^6 + 458752 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (42432 + 26520 z - 40443 z^2 + 147186 z^3 + 3106645 z^4 + 7995488 z^5 + 8759040 z^6 + 4538368 z^7 + 917504 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (8549766225 Pi z^4 Sqrt[1 + Sqrt[1 + 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]