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

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.aasx.01

Input Form

Hypergeometric2F1[-(17/4), 15/4, 5, z] == (1/(8549766225 Pi z^4)) (4096 (4 (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[(1/2) (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[(1/2) (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[(1/2) (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]