Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9gp)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a9gp.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(1/2), 23/4}, -z] == -((1/(824633720832 z^(19/4))) (209 (Sqrt[Pi] (97692469875 + 34735100400 z + 8915961600 z^2 + 2612736000 z^3 + 1548288000 z^4 - 2972712960 z^5 + 3170893824 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (32564156625 - 3308104800 z + 84913920 z^2 + 170311680 z^3 - 216072192 z^4 + 195035136 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (-97692469875 + 69470200800 z + 1669973760 z^2 + 449003520 z^3 - 309657600 z^4 + 182452224 z^5 + 16777216 z^6) 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]