Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8r3)

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=13/4

http://functions.wolfram.com/07.23.03.a8r3.01

Input Form

Hypergeometric2F1[-(21/4), 13/4, 6, -z] == (1/(168441498225 Pi z^5)) (16384 (1 + z)^(1/4) (2 (452608 + 1944800 z + 2012647 z^2 - 1070524 z^3 + 2100826 z^4 + 45448876 z^5 + 110226215 z^6 + 126729064 z^7 + 80204432 z^8 + 27099072 z^9 + 3843840 z^10) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (452608 + 1605344 z + 861679 z^2 - 1548547 z^3 + 3302845 z^4 + 22220671 z^5 + 36830288 z^6 + 29363488 z^7 + 11787776 z^8 + 1921920 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (452608 + 1944800 z + 2012647 z^2 - 1070524 z^3 + 2100826 z^4 + 45448876 z^5 + 110226215 z^6 + 126729064 z^7 + 80204432 z^8 + 27099072 z^9 + 3843840 z^10) 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]