Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aao8)

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=9/4

http://functions.wolfram.com/07.23.03.aao8.01

Input Form

Hypergeometric2F1[-(17/4), 9/4, 5, z] == (1/(3886257375 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] ((-84864 + 392496 z - 487305 z^2 - 357357 z^3 + 3947405 z^4 - 6407247 z^5 + 4954488 z^6 - 1940400 z^7 + 310464 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 2 (-42432 + 42432 Sqrt[z] + 164424 z - 164424 z^(3/2) - 125307 z^2 + 125307 z^(5/2) - 255255 z^3 + 255255 z^(7/2) + 825055 z^4 - 825055 z^(9/2) - 861861 z^5 + 861861 z^(11/2) + 413952 z^6 - 413952 z^(13/2) - 77616 z^7 + 77616 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]