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

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=-11/4, b>=a

For fixed z and a=-11/4, b=-11/4

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

Input Form

Hypergeometric2F1[-(11/4), -(11/4), 6, z] == (1/(51507980123985 Pi z^5)) (16384 (2 Sqrt[1 - z] (157696 - 2279200 z + 16717239 z^2 - 89932535 z^3 + 510099590 z^4 + 3819722994 z^5 + 2325261715 z^6 + 192399701 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (157696 - 2279200 z + 16717239 z^2 - 89932535 z^3 + 510099590 z^4 + 3819722994 z^5 + 2325261715 z^6 + 192399701 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (-157696 + 2397472 z - 18415551 z^2 + 102315290 z^3 - 576443945 z^4 + 2844620076 z^5 + 8104809983 z^6 + 2944347706 z^7 + 140821065 z^8) EllipticK[(1/2) (1 - 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]