Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9130)

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=-15/4

http://functions.wolfram.com/07.23.03.9130.01

Input Form

Hypergeometric2F1[-(23/4), -(15/4), 6, z] == (1/(153738158829255 Pi z^5)) (16384 (-2 Sqrt[1 - z] (-22528 + 517088 z - 6383377 z^2 + 62141387 z^3 - 697398625 z^4 - 15264061897 z^5 - 33273291583 z^6 - 18986495263 z^7 - 2687530987 z^8 - 26316675 z^9 + 429660 z^10) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (-22528 + 533984 z - 6769609 z^2 + 66893288 z^3 - 743572060 z^4 + 4021678808 z^5 + 44492397866 z^6 + 65390114264 z^7 + 26082105572 z^8 + 2453358600 z^9 + 107415 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-22528 + 517088 z - 6383377 z^2 + 62141387 z^3 - 697398625 z^4 - 15264061897 z^5 - 33273291583 z^6 - 18986495263 z^7 - 2687530987 z^8 - 26316675 z^9 + 429660 z^10) 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]