Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9327)

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`=-3/2

http://functions.wolfram.com/07.22.03.9327.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(3/2), 13/4}, -z] == (1/(507343011840 z^(9/4))) (Sqrt[Pi] (51326611875 + 76647740400 z + 334462867200 z^2 - 424714752000 z^3 + 323592192000 z^4 + 282407731200 z^5 + 20082327552 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((51326611875 + 21899354400 z + 12938123520 z^2 - 7756922880 z^3 - 16535715840 z^4 - 1239416832 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (17108870625 + 17728048800 z - 25763754240 z^2 + 17387274240 z^3 + 17422024704 z^4 + 1251999744 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]