Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8991)

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=-21/4

http://functions.wolfram.com/07.23.03.8991.01

Input Form

Hypergeometric2F1[-(23/4), -(21/4), 1, -z] == (1/(334639305 Pi)) (2 (1 + z)^(1/4) (-32 (-46522243 + 1036643913 z - 4150004670 z^2 + 4458646514 z^3 - 1306766895 z^4 + 74378325 z^5) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (-744355888 - 409716583 Sqrt[1 + z] + 105 z^5 (11333840 + 439569 Sqrt[1 + z]) - 105 z^4 (199126384 + 23784203 Sqrt[1 + z]) - 42 z^2 (1580954160 + 473938679 Sqrt[1 + z]) + 14 z^3 (5095596016 + 1047318715 Sqrt[1 + z]) + 3 z (5528767536 + 2256917023 Sqrt[1 + z])) 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]