Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ib)

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=-19/4, b>=a

For fixed z and a=-19/4, b=7/4

http://functions.wolfram.com/07.23.03.a9ib.01

Input Form

Hypergeometric2F1[-(19/4), 7/4, 5, -z] == (1/(2112315975 Pi z^4)) (4096 (1 + z)^(1/4) (4 (13376 + 85272 z + 197505 z^2 + 87780 z^3 + 251190 z^4 + 281628 z^5 + 172641 z^6 + 56880 z^7 + 7920 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - 2 (13376 + 85272 z + 197505 z^2 + 87780 z^3 + 251190 z^4 + 281628 z^5 + 172641 z^6 + 56880 z^7 + 7920 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-26752 - 150480 z - 285285 z^2 + 21945 z^3 + 485145 z^4 + 735219 z^5 + 540120 z^6 + 203760 z^7 + 31680 z^8) 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]