Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8968)

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=-11/2

http://functions.wolfram.com/07.23.03.8968.01

Input Form

Hypergeometric2F1[-(23/4), -(11/2), 1, z] == (2 (1 - z)^(1/4) (32347904 + 671723728 z + 2542147008 z^2 + 2577806704 z^3 + 703032176 z^4 + 35598255 z^5) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (32347904 + 671723728 z + 2542147008 z^2 + 2577806704 z^3 + 703032176 z^4 + 35598255 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (32347904 + 671723728 z + 2542147008 z^2 + 2577806704 z^3 + 703032176 z^4 + 35598255 z^5) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (32347904 + 671723728 z + 2542147008 z^2 + 2577806704 z^3 + 703032176 z^4 + 35598255 z^5) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (32347904 + 671723728 z + 2542147008 z^2 + 2577806704 z^3 + 703032176 z^4 + 35598255 z^5) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-12966080 - 45022320 z + 994748432 z^2 + 3098225840 z^3 + 2156334708 z^4 + 362819611 z^5 + 8515584 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (4845456 Sqrt[2] Pi Sqrt[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]