Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8ff)

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=-3/4

http://functions.wolfram.com/07.23.03.a8ff.01

Input Form

Hypergeometric2F1[-(21/4), -(3/4), 6, -z] == (1/(809698281967575 Pi z^5)) (16384 (1 + z)^(1/4) (-2 (4073472 + 59256288 z + 428685855 z^2 + 2189741814 z^3 + 10912141305 z^4 - 126153295136 z^5 + 46774527921 z^6 + 5702496030 z^7 + 961250983 z^8 + 123155340 z^9 + 8075760 z^10) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (4073472 + 56201184 z + 387012327 z^2 + 1905889635 z^3 + 9525698910 z^4 - 34249899266 z^5 + 2461131123 z^6 + 427712439 z^7 + 57876280 z^8 + 4037880 z^9) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + (4073472 + 59256288 z + 428685855 z^2 + 2189741814 z^3 + 10912141305 z^4 - 126153295136 z^5 + 46774527921 z^6 + 5702496030 z^7 + 961250983 z^8 + 123155340 z^9 + 8075760 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]