Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5mt)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-47/8, b>=a

For fixed z and a=-47/8, b=37/8

http://functions.wolfram.com/07.23.03.b5mt.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, 11/2, z] == (1/(21805087147635 z^(9/2))) (512 ((1 + Sqrt[z])^(27/4) (60051712 - 405349056 Sqrt[z] + 1592978896 z - 4731485112 z^(3/2) + 11795838489 z^2 - 26023168116 z^(5/2) + 52568303568 z^3 - 99368425728 z^(7/2) + 180335291136 z^4 - 299033551872 z^(9/2) + 395458854912 z^5 - 368612868096 z^(11/2) + 220630941696 z^6 - 75443208192 z^(13/2) + 11176771584 z^7) - (1 - Sqrt[z])^(27/4) (60051712 + 405349056 Sqrt[z] + 1592978896 z + 4731485112 z^(3/2) + 11795838489 z^2 + 26023168116 z^(5/2) + 52568303568 z^3 + 99368425728 z^(7/2) + 180335291136 z^4 + 299033551872 z^(9/2) + 395458854912 z^5 + 368612868096 z^(11/2) + 220630941696 z^6 + 75443208192 z^(13/2) + 11176771584 z^7)))

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]