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

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=-37/8, b>=a

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

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

Input Form

Hypergeometric2F1[-(37/8), 47/8, -(11/2), z] == (1/578248704) ((1/(1 - Sqrt[z])^(27/4)) (289124352 - 1951589376 Sqrt[z] + 7039192320 z - 18525314304 z^(3/2) + 40003224352 z^2 - 75167993628 z^(5/2) + 127026574857 z^3 - 196868554740 z^(7/2) + 282879943632 z^4 - 378445706496 z^(9/2) + 469748767488 z^5 - 532783899648 z^(11/2) + 526206320640 z^6 - 412290514944 z^(13/2) + 227101704192 z^7 - 75443208192 z^(15/2) + 11176771584 z^8) + (1/(1 + Sqrt[z])^(27/4)) (289124352 + 1951589376 Sqrt[z] + 7039192320 z + 18525314304 z^(3/2) + 40003224352 z^2 + 75167993628 z^(5/2) + 127026574857 z^3 + 196868554740 z^(7/2) + 282879943632 z^4 + 378445706496 z^(9/2) + 469748767488 z^5 + 532783899648 z^(11/2) + 526206320640 z^6 + 412290514944 z^(13/2) + 227101704192 z^7 + 75443208192 z^(15/2) + 11176771584 z^8))

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]