Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9798)

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=11/4

http://functions.wolfram.com/07.23.03.9798.01

Input Form

Hypergeometric2F1[-(23/4), 11/4, 6, z] == (1/(4959295446105 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((9844736 - 57684000 z + 110767701 z^2 - 26823060 z^3 - 63596610 z^4 + 373781772 z^5 - 651704235 z^6 + 606707712 z^7 - 327412800 z^8 + 97194240 z^9 - 12355200 z^10) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-9844736 + 9844736 Sqrt[z] + 50300448 z - 50300448 z^(3/2) - 74196045 z^2 + 74196045 z^(5/2) - 23362020 z^3 + 23362020 z^(7/2) + 39369330 z^4 - 39369330 z^(9/2) + 256127508 z^5 - 256127508 z^(11/2) - 711288669 z^6 + 711288669 z^(13/2) + 831855960 z^7 - 831855960 z^(15/2) - 524787120 z^8 + 524787120 z^(17/2) + 175855680 z^9 - 175855680 z^(19/2) - 24710400 z^10 + 24710400 z^(21/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

Standard Form

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MathML Form

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</semantics> </math>

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]