Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8yu)

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=-21/4, b>=a

For fixed z and a=-21/4, b=23/4

http://functions.wolfram.com/07.23.03.a8yu.01

Input Form

Hypergeometric2F1[-(21/4), 23/4, 3, z] == -((1/(10548412875 Pi z^2)) (64 (2 (204204 + 5564559 z - 594932735 z^2 + 4864493600 z^3 - 14984243200 z^4 + 21756903424 z^5 - 15074328576 z^6 + 4026531840 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (-204204 (1 + Sqrt[1 - z]) - 51051 (109 + 110 Sqrt[1 - z]) z + 5 (118986547 + 52773400 Sqrt[1 - z]) z^2 - 800 (6080617 + 1930032 Sqrt[1 - z]) z^3 + 51200 (292661 + 64928 Sqrt[1 - z]) z^4 - 1048576 (20749 + 2904 Sqrt[1 - z]) z^5 + 25165824 (599 + 40 Sqrt[1 - z]) z^6 - 4026531840 z^7) 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]