Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9129)

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/07.23.03.9129.01

Input Form

Hypergeometric2F1[-(23/4), -(15/4), 11/2, z] == (32 (2 (-56530320 + 1358746620 z - 18151919401 z^2 + 207701379963 z^3 - 3969647399025 z^4 - 38914517252545 z^5 - 68772939709215 z^6 - 34312587623727 z^7 - 4278847585099 z^8 - 26093442375 z^9 + 444143700 z^10) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-56530320 + 1358746620 z - 18151919401 z^2 + 207701379963 z^3 - 3969647399025 z^4 - 38914517252545 z^5 - 68772939709215 z^6 - 34312587623727 z^7 - 4278847585099 z^8 - 26093442375 z^9 + 444143700 z^10) EllipticE[(1/2) (1 + Sqrt[z])] - (-56530320 - 28265160 Sqrt[z] + 1358746620 z + 677017880 z^(3/2) - 18151919401 z^2 - 9020522973 z^(5/2) + 207701379963 z^3 + 103121903115 z^(7/2) - 3969647399025 z^4 - 10008833121265 z^(9/2) - 38914517252545 z^5 - 50104807916505 z^(11/2) - 68772939709215 z^6 - 63395929302135 z^(13/2) - 34312587623727 z^7 - 24361856678431 z^(15/2) - 4278847585099 z^8 - 2306771341875 z^(17/2) - 26093442375 z^9 + 111035925 z^(19/2) + 444143700 z^10) EllipticK[(1/2) (1 - Sqrt[z])] + (-56530320 + 28265160 Sqrt[z] + 1358746620 z - 677017880 z^(3/2) - 18151919401 z^2 + 9020522973 z^(5/2) + 207701379963 z^3 - 103121903115 z^(7/2) - 3969647399025 z^4 + 10008833121265 z^(9/2) - 38914517252545 z^5 + 50104807916505 z^(11/2) - 68772939709215 z^6 + 63395929302135 z^(13/2) - 34312587623727 z^7 + 24361856678431 z^(15/2) - 4278847585099 z^8 + 2306771341875 z^(17/2) - 26093442375 z^9 - 111035925 z^(19/2) + 444143700 z^10) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)/ (257033705267625 Pi^(3/2) z^(9/2))

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]