Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9621)

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/07.22.03.9621.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, 19/4}, -z] == ((2 Sqrt[z] (-25329323674029375 + 71386420505400000 z - 72192585796531200 z^2 + 206616030949785600 z^3 + 69438154928947200 z^4 + 5454160283566080 z^5 + 146079555256320 z^6 + 1431297851392 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (-75987971022088125 + 144103774274460000 z - 129771870055027200 z^2 + 170887766495846400 z^3 + 66258692466278400 z^4 + 5365214729994240 z^5 + 145192208302080 z^6 + 1428613496832 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-63397039863031875 + 107210304205804800 z - 104472384349132800 z^2 + 191143383795302400 z^3 + 68129122487500800 z^4 + 5418191589212160 z^5 + 145723408515072 z^6 + 1430224109568 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(248119806984192000 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]