Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9472)

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`=3/2

http://functions.wolfram.com/07.22.03.9472.01

Input Form

HypergeometricPFQ[{-(19/4)}, {3/2, 15/4}, z] == ((2 Sqrt[z] (481225870125 - 1099944846000 z + 146935188691200 z^2 - 194938626355200 z^3 + 43007002214400 z^4 - 2608296099840 z^5 + 50247761920 z^6 - 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 + (-1443677610375 + 1099944846000 z - 73916293651200 z^2 + 171897726873600 z^3 - 41458094899200 z^4 + 2577342136320 z^5 - 50079989760 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (1443677610375 - 4179790414800 z - 111046980844800 z^2 + 185118248448000 z^3 - 42374062080000 z^4 + 2595839016960 z^5 - 50180653056 z^6 + 268435456 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(240204496896000 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]