Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9521)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.9521.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, 15/4}, -z] == ((2 Sqrt[z] (-2406129350625 - 38498069610000 z + 688113206726400 z^2 + 536407816089600 z^3 + 82528955596800 z^4 + 3833557155840 z^5 + 59810775040 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - (-7218388051875 - 104494760370000 z + 455299523078400 z^2 + 490612502016000 z^3 + 80230322995200 z^4 + 3796626309120 z^5 + 59643002880 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (7218388051875 - 98749166115600 z + 580218749510400 z^2 + 517167963648000 z^3 + 81593435750400 z^4 + 3818709319680 z^5 + 59743666176 z^6 + 268435456 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1000852070400000 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]