Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9go)

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=-19/4, b>=a

For fixed z and a=-19/4, b=5/4

http://functions.wolfram.com/07.23.03.a9go.01

Input Form

Hypergeometric2F1[-(19/4), 5/4, 6, z] == (1/(38444150745 Pi z^5)) (16384 (2 Sqrt[1 - z] (-38912 + 333792 z - 1243113 z^2 + 2561048 z^3 - 2765070 z^4 + 3914148 z^5 - 2958193 z^6 + 1360332 z^7 - 356352 z^8 + 40960 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (-38912 + 362976 z - 1490721 z^2 + 3471167 z^3 - 4608450 z^4 + 1149078 z^5 - 824509 z^6 + 363819 z^7 - 91968 z^8 + 10240 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-38912 + 333792 z - 1243113 z^2 + 2561048 z^3 - 2765070 z^4 + 3914148 z^5 - 2958193 z^6 + 1360332 z^7 - 356352 z^8 + 40960 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]