Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8391)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8391.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(11/4)}, -z] == (1/(2462332672800 z^(5/2))) (-2 Sqrt[z] (948702429675 + 361410449400 z - 71818306560 z^2 + 14370048000 z^3 - 5093130240 z^4 + 6494355456 z^5 + 394002432 z^6 + 4194304 z^7) Cos[2 Sqrt[z]] - 262144 Sqrt[Pi] z^(25/4) (418209 + 24288 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (948702429675 - 903526123500 z + 340151011200 z^2 - 61599605760 z^3 + 15441592320 z^4 - 9057337344 z^5 + 54232350720 z^6 + 3177185280 z^7 + 33554432 z^8) Sin[2 Sqrt[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,a₂},{b₁},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]