Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7gl)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-31/8

http://functions.wolfram.com/07.23.03.b7gl.01

Input Form

Hypergeometric2F1[-(43/8), -(31/8), 11/2, -z] == -((1024 (4 Sqrt[z] (-2800 - 66250 z - 868155 z^2 - 9689100 z^3 - 797319328 z^4 + 4268836832 z^5 - 5939597070 z^6 + 2680558860 z^7 - 355416360 z^8 + 7123306 z^9 + 67201 z^10) Cos[(5 ArcTan[Sqrt[z]])/4] + (8960 + 210320 z + 2738619 z^2 + 30490584 z^3 + 566511540 z^4 - 9054863480 z^5 + 23279424610 z^6 - 18370032792 z^7 + 4633984308 z^8 - 283073240 z^9 - 336005 z^10) Sin[(5 ArcTan[Sqrt[z]])/4]))/ (2533349278889 z^(9/2) (1 + z)^(5/8)))

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]