Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9sh)

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=25/8, b>=a

For fixed z and a=25/8, b=39/8

http://functions.wolfram.com/07.23.03.c9sh.01

Input Form

Hypergeometric2F1[25/8, 39/8, -(9/2), z] == (1/(15332352 (1 - z)^(25/2))) (2 Sqrt[1 - z] (7666176 - 118186880 z + 910864630 z^2 - 4926984721 z^3 + 24037856692 z^4 - 193798977799 z^5 - 537458938170 z^6 - 199666485855 z^7 - 6493984848 z^8 + 135291351 z^9) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (3833088 - 60291280 z + 473389933 z^2 - 2598263264 z^3 + 12732656319 z^4 - 2767212846242 z^5 - 3701655013845 z^6 - 867805821756 z^7 - 13123261047 z^8 + 270582702 z^9) Sin[ArcSin[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]