Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8419)

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/07.22.03.8419.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 17/4}, -z] == (Sqrt[Pi] (-340465584449615625 + 5447449351193850000 z - 13945470339056256000 z^2 + 57847876962011136000 z^3 + 35598693515083776000 z^4 + 4786378960011264000 z^5 + 221016055873536000 z^6 + 4041436450258944 z^7 + 29338921598976 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((340465584449615625 - 1201284689814316800 z + 2288970350029440000 z^2 + 1988032127792578560 z^3 + 287072698542981120 z^4 + 13583327743180800 z^5 + 250886555172864 z^6 + 1829656068096 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] - 4 Sqrt[z] (462677465782518525 - 1095442476957259200 z + 3292709932866816000 z^2 + 2173906662085509120 z^3 + 296657733618892800 z^4 + 13766884105125888 z^5 + 252247724261376 z^6 + 1832877293568 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/ (55466634448679731200 z^(13/4))

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,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]