Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aai6)

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.aai6.01

Input Form

Hypergeometric2F1[-(17/4), 1/4, 6, -z] == (1/(18031456968525 Pi z^5)) (16384 (1 + z)^(1/4) (2 (-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[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-1357824 - 13641888 z - 64175085 z^2 - 195969540 z^3 - 517730070 z^4 + 204474732 z^5 + 60938339 z^6 + 12523280 z^7 + 1228920 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + 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) EllipticK[1/2 - 1/(2 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]