Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aai5)

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=-17/4, b>=a

For fixed z and a=-17/4, b=1/4

http://functions.wolfram.com/07.23.03.aai5.01

Input Form

Hypergeometric2F1[-(17/4), 1/4, 6, z] == (1/(18031456968525 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((1357824 - 14660256 z + 74247381 z^2 - 242561865 z^3 + 657755670 z^4 + 2037716142 z^5 - 519834623 z^6 + 144750683 z^7 - 27299580 z^8 + 2457840 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-1357824 + 1357824 Sqrt[z] + 13641888 z - 13641888 z^(3/2) - 64175085 z^2 + 64175085 z^(5/2) + 195969540 z^3 - 195969540 z^(7/2) - 517730070 z^4 + 517730070 z^(9/2) - 204474732 z^5 + 204474732 z^(11/2) + 60938339 z^6 - 60938339 z^(13/2) - 12523280 z^7 + 12523280 z^(15/2) + 1228920 z^8 - 1228920 z^(17/2)) 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]