Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8413)

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/07.22.03.8413.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 11/4}, -z] == ((2 z (-2260051013595375 + 44381404105038000 z + 39922232967302400 z^2 + 7529674673664000 z^3 + 460945376870400 z^4 + 10703890022400 z^5 + 95546245120 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (-5994404204914125 + 28088182344222000 z + 35879902368710400 z^2 + 7258493387059200 z^3 + 454412810649600 z^4 + 10644624506880 z^5 + 95378472960 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 (589311626904000 - 5791828333165875 z + 36664069638596400 z^2 + 38201859830534400 z^3 + 7418448657100800 z^4 + 458306232975360 z^5 + 10680108318720 z^6 + 95479136256 z^7 + 268435456 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(65849810906880000 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]