Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a88c)

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=-15/4

http://functions.wolfram.com/07.23.03.a88c.01

Input Form

Hypergeometric2F1[-(21/4), -(15/4), 3, -z] == (1/(48522699225 Pi z^2)) (64 (1 + z)^(1/4) (4 (-306306 - 12711699 z + 1331614096 z^2 - 6628154265 z^3 + 7544875590 z^4 - 2116409477 z^5 + 84391692 z^6 + 1110417 z^7) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-612612 - 24963939 z + 1165545005 z^2 - 4087650750 z^3 + 3105383190 z^4 - 474329359 z^5 + 1110417 z^6) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - 2 (-306306 - 12711699 z + 1331614096 z^2 - 6628154265 z^3 + 7544875590 z^4 - 2116409477 z^5 + 84391692 z^6 + 1110417 z^7) 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]