Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5ll)

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.b5ll.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, -(9/2), -z] == (1/(1870848 (1 + z)^(25/8))) ((-(-1870848 + 5508608 z - 15372900 z^2 + 48980971 z^3 - 214961253 z^4 + 2306859984 z^5 + 20409362688 z^6 + 43807948800 z^7 + 37170118656 z^8 + 11176771584 z^9)) Cos[ArcTan[Sqrt[z]]/4] + Sqrt[z] (467712 - 1523312 z + 4357627 z^2 - 13751829 z^3 + 58472700 z^4 + 3002368512 z^5 + 8550153216 z^6 + 8419344384 z^7 + 2794192896 z^8) Sin[ArcTan[Sqrt[z]]/4])

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]