Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9606)

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=5/4

http://functions.wolfram.com/07.23.03.9606.01

Input Form

Hypergeometric2F1[-(23/4), 5/4, 5, z] == (1/(12814716915 Pi z^4)) (4096 (-2 Sqrt[1 - z] (-55936 + 468464 z - 1656667 z^2 + 2826516 z^3 - 6140554 z^4 + 6962900 z^5 - 4972275 z^6 + 2228864 z^7 - 575488 z^8 + 65536 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] + 2 (-27968 + 255208 z - 1002041 z^2 + 2018940 z^3 - 950390 z^4 + 1014412 z^5 - 691257 z^6 + 297784 z^7 - 74240 z^8 + 8192 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-55936 + 468464 z - 1656667 z^2 + 2826516 z^3 - 6140554 z^4 + 6962900 z^5 - 4972275 z^6 + 2228864 z^7 - 575488 z^8 + 65536 z^9) 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]