Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9721)

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=9/4

http://functions.wolfram.com/07.23.03.9721.01

Input Form

Hypergeometric2F1[-(23/4), 9/4, 2, -z] == (1/(4542615 Pi z Sqrt[1 + Sqrt[1 + z]])) (8 Sqrt[2] (Sqrt[1 + z] (33649 + 1888830 z + 9130653 z^2 + 18191168 z^3 + 18224640 z^4 + 9142272 z^5 + 1835008 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (33649 + 1922479 z + 11019483 z^2 + 27321821 z^3 + 36415808 z^4 + 27366912 z^5 + 10977280 z^6 + 1835008 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (33649 + 778413 z + 3127671 z^2 + 5570267 z^3 + 5139840 z^4 + 2414592 z^5 + 458752 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (33649 + 1888830 z + 9130653 z^2 + 18191168 z^3 + 18224640 z^4 + 9142272 z^5 + 1835008 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))

Standard Form

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MathML Form

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</cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]