Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8409)

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`=7/2

http://functions.wolfram.com/07.22.03.8409.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 7/4}, -z] == ((2 z (-1636976741400 + 588711763314675 z + 840134708899200 z^2 + 220180472328960 z^3 + 17299061145600 z^4 + 490718429184 z^5 + 5175771136 z^6 + 16777216 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (-9821860448400 + 292931141528025 z + 726620613919200 z^2 + 210135220289280 z^3 + 17000860631040 z^4 + 487511752704 z^5 + 5165285376 z^6 + 16777216 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 (-3683197668150 - 24554651121000 z + 440434438619175 z^2 + 791034668424000 z^3 + 216038179019520 z^4 + 17178372440064 z^5 + 489431040000 z^6 + 5171576832 z^7 + 16777216 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(960309742392000 Sqrt[2] z^(7/4))

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]