Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8477)

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`=11/2

http://functions.wolfram.com/07.22.03.8477.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(21/4)}, -z] == ((4 z (30561470771387180625 + 447787117529482500 z + 338689892531390400 z^2 + 252842696772019200 z^3 - 72581192268595200 z^4 + 7432304901488640 z^5 - 427389616128000 z^6 + 16600652578816 z^7 - 503584915456 z^8 + 17179869184 z^9) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (91684412314161541875 - 16120336231061370000 z - 147013744560328800 z^2 + 160949306300428800 z^3 - 39137467803033600 z^4 + 3867923697500160 z^5 - 219405373931520 z^6 + 8472124981248 z^7 - 257161166848 z^8 + 8589934592 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (275053236942484625625 - 100752101444133562500 z + 6048964261941123600 z^2 + 838020365072352000 z^3 + 1101230490924748800 z^4 - 298607301638553600 z^5 + 30187536824401920 z^6 - 1727072468729856 z^7 + 66933038776320 z^8 - 2031519531008 z^9 + 68719476736 z^10) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(428838579160992000 Sqrt[2] z^(15/4))

Standard Form

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MathML Form

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type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]