Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b67d)

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=-35/8

http://functions.wolfram.com/07.23.03.b67d.01

Input Form

Hypergeometric2F1[-(45/8), -(35/8), 9/2, -z] == -((256 (Sqrt[z] Sqrt[1 + z] (-772560 - 22149939 z - 411880707 z^2 - 44844601729 z^3 + 346024222577 z^4 - 673794615315 z^5 + 424792822711 z^6 - 82142104667 z^7 + 3181567851 z^8 + 15482082 z^9) Cosh[(3 ArcSinh[Sqrt[z]])/4] + 2 (515040 + 15206556 z + 287183085 z^2 + 7906784634 z^3 - 96351816486 z^4 + 150860101034 z^5 + 71001882996 z^6 - 145085894610 z^7 + 37171519574 z^8 - 1594654446 z^9 - 7741041 z^10) Sinh[(3 ArcSinh[Sqrt[z]])/4]))/ (8533891320955 z^(7/2) Sqrt[1 + z]))

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]