Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8487)

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`=11/2

http://functions.wolfram.com/07.22.03.8487.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(11/4)}, -z] == (-2 Sqrt[z] (24073324153003125 - 6324682864500000 z - 394660210744800 z^2 + 77100895872000 z^3 - 9815998832640 z^4 + 1663232901120 z^5 - 543739084800 z^6 + 666458128384 z^7 + 31390171136 z^8 + 268435456 z^9) Cos[2 Sqrt[z]] - 16777216 Sqrt[Pi] z^(33/4) (662929 + 30176 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (24073324153003125 - 38422448401837500 z - 521153868034800 z^2 - 408634748121600 z^3 + 54424161792000 z^4 - 7624513290240 z^5 + 1704905932800 z^6 - 944322379776 z^7 + 5514469572608 z^8 + 252731981824 z^9 + 2147483648 z^10) Sin[2 Sqrt[z]])/ (948662518003200 z^(9/2))

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]