Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8033)

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/07.22.03.8033.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 15/4}, -z] == ((-2 Sqrt[z] (1604888276866875 - 758961943740000 z - 1151003939904000 z^2 + 593630740684800 z^3 - 101953614643200 z^4 + 9852703211520 z^5 - 693737881600 z^6 + 53150220288 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 + (4814664830600625 - 9613517954040000 z - 1619118813312000 z^2 + 675532376064000 z^3 - 109224699494400 z^4 + 10325600501760 z^5 - 719742566400 z^6 + 50465865728 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (4814664830600625 + 657767017908000 z + 1349265677760000 z^2 - 623820369715200 z^3 + 104705556480000 z^4 - 10038993223680 z^5 + 705347715072 z^6 - 52076478464 z^7 - 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(2365090430976000 Sqrt[2] z^(9/4))

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]