Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6iq)

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=-3/8

http://functions.wolfram.com/07.23.03.b6iq.01

Input Form

Hypergeometric2F1[-(45/8), -(3/8), 11/2, z] == (1/(31048838635815 z^(9/2))) (1024 (-2 Sqrt[z] (-3605280 + 50581220 z - 355966677 z^2 + 1841763726 z^3 - 27502181047 z^4 - 29135284776 z^5 + 3749185725 z^6 - 996587194 z^7 + 225563967 z^8 - 34258224 z^9 + 2521168 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) ((9614080 - 143095280 z + 1064135947 z^2 - 5717845320 z^3 + 37076657673 z^4 + 22855873722 z^5 - 61796265427 z^6 + 8442652964 z^7 - 2210488945 z^8 + 484755866 z^9 - 71037616 z^10 + 5042336 z^11) Sin[(3 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]