Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9189)

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`=-9/2

http://functions.wolfram.com/07.22.03.9189.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 19/4}, -z] == ((2 Sqrt[z] (-25329323674029375 + 19458024325740000 z + 1724713518528000 z^2 + 1427976384307200 z^3 - 464230416384000 z^4 + 51913666068480 z^5 - 3179450204160 z^6 + 129385889792 z^7 - 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 + (75987971022088125 - 174165266915640000 z + 1971101164032000 z^2 - 1877239203840000 z^3 + 504192555417600 z^4 - 54168114954240 z^5 + 3267530588160 z^6 - 132070244352 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (75987971022088125 - 12057595401852000 z + 950352346944000 z^2 + 1573992870912000 z^3 - 478769047142400 z^4 + 52766976245760 z^5 - 3213474398208 z^6 + 130459631616 z^7 - 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (2522763126374400 Sqrt[2] 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]