Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9995)

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=17/4

http://functions.wolfram.com/07.23.03.9995.01

Input Form

Hypergeometric2F1[-(23/4), 17/4, 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (-9844736 - 14305632 z + 14983419 z^2 - 24212859 z^3 + 79849077 z^4 + 1690585143 z^5 + 4984514604 z^6 + 6787448832 z^7 + 4966883328 z^8 + 1904214016 z^9 + 301989888 z^10) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-9844736 - 24150368 z + 677787 z^2 - 9229440 z^3 + 55636218 z^4 + 1770434220 z^5 + 6675099747 z^6 + 11771963436 z^7 + 11754332160 z^8 + 6871097344 z^9 + 2206203904 z^10 + 301989888 z^11) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-9844736 - 21689184 z + 4946403 z^2 - 12286692 z^3 + 60366306 z^4 + 628521756 z^5 + 1596298323 z^6 + 1990601664 z^7 + 1365878784 z^8 + 497287168 z^9 + 75497472 z^10) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (-9844736 - 14305632 z + 14983419 z^2 - 24212859 z^3 + 79849077 z^4 + 1690585143 z^5 + 4984514604 z^6 + 6787448832 z^7 + 4966883328 z^8 + 1904214016 z^9 + 301989888 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (9210120114195 Pi z^5 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]