Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8380)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=7/3, b>=a

For fixed z and a=7/3, b=17/3

http://functions.wolfram.com/07.23.03.8380.01

Input Form

Hypergeometric2F1[7/3, 17/3, -(7/2), -z] == (1/(3981312 (1 + z)^(23/2))) ((3981312 + 61046784 z + 483491840 z^2 + 2957115392 z^3 + 25764642816 z^4 - 109168358387 z^5 + 48894052756 z^6 + 593256480 z^7 + 52975808 z^8 + 2902784 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-1327104 - 19415040 z - 147603456 z^2 - 883277824 z^3 + 32551558105 z^4 - 26426504596 z^5 + 567857120 z^6 + 51524416 z^7 + 2902784 z^8) Sinh[ArcSinh[Sqrt[z]]/3])

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]