Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9473)

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=-23/4, b>=a

For fixed z and a=-23/4, b=1/4

http://functions.wolfram.com/07.23.03.9473.01

Input Form

Hypergeometric2F1[-(23/4), 1/4, 5/2, z] == (1/(16823625 Pi^(3/2) z^(3/2))) (4 (4 (100947 - 1817046 z - 2029510 z^2 + 1819160 z^3 - 1283365 z^4 + 603734 z^5 - 166912 z^6 + 20480 z^7) EllipticE[(1/2) (1 - Sqrt[z])] - 4 (100947 - 1817046 z - 2029510 z^2 + 1819160 z^3 - 1283365 z^4 + 603734 z^5 - 166912 z^6 + 20480 z^7) EllipticE[(1/2) (1 + Sqrt[z])] - (201894 + 100947 Sqrt[z] - 3634092 z - 6014540 z^(3/2) - 4059020 z^2 + 767410 z^(5/2) + 3638320 z^3 - 568460 z^(7/2) - 2566730 z^4 + 279955 z^(9/2) + 1207468 z^5 - 80576 z^(11/2) - 333824 z^6 + 10240 z^(13/2) + 40960 z^7) EllipticK[(1/2) (1 - Sqrt[z])] + (201894 - 100947 Sqrt[z] - 3634092 z + 6014540 z^(3/2) - 4059020 z^2 - 767410 z^(5/2) + 3638320 z^3 + 568460 z^(7/2) - 2566730 z^4 - 279955 z^(9/2) + 1207468 z^5 + 80576 z^(11/2) - 333824 z^6 - 10240 z^(13/2) + 40960 z^7) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^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]