Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a94i)

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=-13/4

http://functions.wolfram.com/07.23.03.a94i.01

Input Form

Hypergeometric2F1[-(19/4), -(13/4), 6, z] == (1/(94764831586425 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((38912 - 775200 z + 8130537 z^2 - 65315635 z^3 + 579984405 z^4 + 17498228601 z^5 + 33725440875 z^6 + 15456839031 z^7 + 1516424535 z^8 + 480675 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-38912 + 38912 Sqrt[z] + 746016 z - 746016 z^(3/2) - 7575585 z^2 + 7575585 z^(5/2) + 59719660 z^3 - 59719660 z^(7/2) - 536050515 z^4 + 536050515 z^(9/2) - 6325612146 z^5 + 6325612146 z^(11/2) - 8043576807 z^6 + 8043576807 z^(13/2) - 2240478720 z^7 + 2240478720 z^(15/2) - 87963525 z^8 + 87963525 z^(17/2) + 961350 z^9 - 961350 z^(19/2)) 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]