Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9pp)

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=15/4

http://functions.wolfram.com/07.23.03.a9pp.01

Input Form

Hypergeometric2F1[-(19/4), 15/4, 6, -z] == (1/(12814716915 Pi z^5)) (16384 (1 + z)^(1/4) (2 (38912 + 111264 z + 24985 z^2 - 40565 z^3 + 129675 z^4 + 1042041 z^5 + 1939392 z^6 + 1684800 z^7 + 723840 z^8 + 124800 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (38912 + 111264 z + 24985 z^2 - 40565 z^3 + 129675 z^4 + 1042041 z^5 + 1939392 z^6 + 1684800 z^7 + 723840 z^8 + 124800 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-38912 - 82080 z + 32015 z^2 + 8645 z^3 - 129675 z^4 + 617799 z^5 + 2129400 z^6 + 2442960 z^7 + 1260480 z^8 + 249600 z^9) EllipticK[1/2 - 1/(2 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]