Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7tz)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a7tz.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, 21/4}, -z] == ((2 Sqrt[z] (142711951206825 + 624517256563200 z - 2914413863961600 z^2 + 13476020144209920 z^3 + 12045630546247680 z^4 + 1747319380770816 z^5 + 74078723506176 z^6 + 1050119503872 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]]^2 - 3 (237853252011375 + 1210002184591200 z - 4371620795942400 z^2 + 5100001201152000 z^3 + 10619536036331520 z^4 + 1684022923100160 z^5 + 73166210727936 z^6 + 1046361407488 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (713559756034125 + 2107745740900800 z - 5009567067648000 z^2 + 5962152771993600 z^3 + 10805000112046080 z^4 + 1692781101711360 z^5 + 73295361736704 z^6 + 1046898278400 z^7 + 4294967296 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(9902853020712960 Sqrt[2] z^(15/4))

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]