Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9135)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.9135.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(11/2), 13/4}, -z] == (Sqrt[Pi] (139064322214125 + 100485187664400 z + 178640333625600 z^2 - 69039742464000 z^3 + 8305532928000 z^4 - 483231006720 z^5 + 15619588096 z^6 - 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-139064322214125 + 47850089364000 z - 4954152994560 z^2 + 551567278080 z^3 - 31179079680 z^4 + 991952896 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-46354774071375 - 12304308693600 z + 4427698302720 z^2 - 525201653760 z^3 + 30391861248 z^4 - 979369984 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/ (208348863528960 z^(9/4))

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]