Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5cw)

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=21/8

http://functions.wolfram.com/07.23.03.b5cw.01

Input Form

Hypergeometric2F1[-(47/8), 21/8, 11/2, z] == (1/(3759497784075 z^(9/2))) (512 ((1 + Sqrt[z])^(35/4) (60051712 - 525452480 Sqrt[z] + 2227811280 z - 6258514360 z^(3/2) + 13273539545 z^2 - 22530651696 z^(5/2) + 31189357920 z^3 - 34679863680 z^(7/2) + 29725597440 z^4 - 18561607680 z^(9/2) + 7840960512 z^5 - 1986969600 z^(11/2) + 227082240 z^6) - (1 - Sqrt[z])^(35/4) (60051712 + 525452480 Sqrt[z] + 2227811280 z + 6258514360 z^(3/2) + 13273539545 z^2 + 22530651696 z^(5/2) + 31189357920 z^3 + 34679863680 z^(7/2) + 29725597440 z^4 + 18561607680 z^(9/2) + 7840960512 z^5 + 1986969600 z^(11/2) + 227082240 z^6)))

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]