Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a86c)

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=-21/4, b>=a

For fixed z and a=-21/4, b=-19/4

http://functions.wolfram.com/07.23.03.a86c.01

Input Form

Hypergeometric2F1[-(21/4), -(19/4), 4, z] == (1/(4512611027925 Pi z^3)) (256 Sqrt[1 + Sqrt[z]] ((940576 - 29892681 z + 730210299 z^2 + 60862738203 z^3 + 293832096255 z^4 + 376114869333 z^5 + 146747677377 z^6 + 14916184857 z^7 + 178373349 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-940576 + 940576 Sqrt[z] + 29187249 z - 29187249 z^(3/2) - 708430086 z^2 + 708430086 z^(5/2) - 26135908065 z^3 + 26135908065 z^(7/2) - 91520882100 z^4 + 91520882100 z^(9/2) - 83165041953 z^5 + 83165041953 z^(11/2) - 20810064198 z^6 + 20810064198 z^(13/2) - 1026219663 z^7 + 1026219663 z^(15/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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]