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

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=-13/4, b>=a

For fixed z and a=-13/4, b=19/4

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

Input Form

Hypergeometric2F1[-(13/4), 19/4, 3/2, z] == (1/(533610 Pi^(3/2))) ((-128 (-2025 + 19320 z - 44544 z^2 + 28672 z^3) EllipticE[(1/2) (1 - Sqrt[z])] - 128 (-2025 + 19320 z - 44544 z^2 + 28672 z^3) EllipticE[(1/2) (1 + Sqrt[z])] + (1/Sqrt[z]) ((-7605 - 129600 Sqrt[z] + 178560 z + 1236480 z^(3/2) - 583680 z^2 - 2850816 z^(5/2) + 458752 z^3 + 1835008 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/Sqrt[z]) ((7605 - 129600 Sqrt[z] - 178560 z + 1236480 z^(3/2) + 583680 z^2 - 2850816 z^(5/2) - 458752 z^3 + 1835008 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

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]