Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8433)

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`=9/2

http://functions.wolfram.com/07.22.03.8433.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(17/4)}, -z] == ((-4 z (-3198479410924875 - 613164716564400 z - 572805701740800 z^2 + 255232297267200 z^3 - 40184670781440 z^4 + 3754473553920 z^5 - 275498663936 z^6 + 28722593792 z^7 + 1073741824 z^8) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-9595438232774625 - 11791629164700 z - 432597950769600 z^2 + 145329275520000 z^3 - 21580249743360 z^4 + 1981207019520 z^5 - 145823367168 z^6 + 14025752576 z^7 + 536870912 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (28786314698323875 - 5447732674091400 z + 1006219022054400 z^2 + 2656736390246400 z^3 - 1069735204454400 z^4 + 165055050547200 z^5 - 15330365669376 z^6 + 1129039527936 z^7 - 113816633344 z^8 - 4294967296 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1120658307912000 Sqrt[2] z^(11/4))

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]