Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b75o)

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=-45/8, b>=a

For fixed z and a=-45/8, b=39/8

http://functions.wolfram.com/07.23.03.b75o.01

Input Form

Hypergeometric2F1[-(45/8), 39/8, -(11/2), z] == (1/449748992) ((1/(1 - Sqrt[z])^(19/4)) (224874496 - 1068153856 Sqrt[z] + 3123966720 z - 7161486080 z^(3/2) + 14173641440 z^2 - 25352343492 z^(5/2) + 42180965207 z^3 - 66398994860 z^(7/2) + 100227893040 z^4 - 146298929920 z^(9/2) + 208472712448 z^5 - 291606002688 z^(11/2) + 409271582720 z^6 - 514597191680 z^(13/2) + 456446115840 z^7 - 230055215104 z^(15/2) + 48432676864 z^8) + (1/(1 + Sqrt[z])^(19/4)) (224874496 + 1068153856 Sqrt[z] + 3123966720 z + 7161486080 z^(3/2) + 14173641440 z^2 + 25352343492 z^(5/2) + 42180965207 z^3 + 66398994860 z^(7/2) + 100227893040 z^4 + 146298929920 z^(9/2) + 208472712448 z^5 + 291606002688 z^(11/2) + 409271582720 z^6 + 514597191680 z^(13/2) + 456446115840 z^7 + 230055215104 z^(15/2) + 48432676864 z^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]