Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9ka)

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=-41/8, b>=a

For fixed z and a=-41/8, b=43/8

http://functions.wolfram.com/07.23.03.b9ka.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, 11/2, -z] == -((1024 (Sqrt[z] (1561280 - 3708040 z + 12026735 z^2 - 58795435 z^3 - 3687821571 z^4 - 10990807121 z^5 - 5086423664 z^6 + 19643909376 z^7 + 32918552576 z^8 + 19972685824 z^9 + 4402970624 z^10) Cos[(7 ArcTan[Sqrt[z]])/4] - (892160 - 2732240 z + 8367485 z^2 - 38422125 z^3 + 456503635 z^4 + 12256849633 z^5 + 50469838356 z^6 + 91125931520 z^7 + 84947932160 z^8 + 40249524224 z^9 + 7705198592 z^10) Sin[(7 ArcTan[Sqrt[z]])/4]))/(4552418669799 z^(9/2) (1 + z)^(7/8)))

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]