Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9261)

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/07.23.03.9261.01

Input Form

Hypergeometric2F1[-(23/4), -(9/4), 4, -z] == (1/(217850187555 Pi z^3)) (256 (1 + z)^(1/4) (-2 (153824 + 3504303 z + 57539790 z^2 - 2704163511 z^3 + 6385760136 z^4 - 2658260367 z^5 + 9532614 z^6 + 785655 z^7 + 39780 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (153824 + 3504303 z + 57539790 z^2 - 2704163511 z^3 + 6385760136 z^4 - 2658260367 z^5 + 9532614 z^6 + 785655 z^7 + 39780 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-153824 - 3388935 z - 55016115 z^2 + 1043080626 z^3 - 1563240798 z^4 + 311192973 z^5 + 17937465 z^6 + 1511640 z^7 + 79560 z^8) EllipticK[1/2 - 1/(2 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]