Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a91q)

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=-19/4, b>=a

For fixed z and a=-19/4, b=-17/4

http://functions.wolfram.com/07.23.03.a91q.01

Input Form

Hypergeometric2F1[-(19/4), -(17/4), 3, z] == (1/(15058768725 Pi z^2)) (64 Sqrt[1 + Sqrt[z]] (4 (-46189 + 1939938 z + 207213465 z^2 + 1060423500 z^3 + 1266238485 z^4 + 393743538 z^5 + 23277279 z^6) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (184756 - 184756 Sqrt[z] - 7621185 z + 7621185 z^(3/2) - 363961575 z^2 + 363961575 z^(5/2) - 1319483370 z^3 + 1319483370 z^(7/2) - 1066700250 z^4 + 1066700250 z^(9/2) - 191545317 z^5 + 191545317 z^(11/2) - 3663075 z^6 + 3663075 z^(13/2)) 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]