Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9448)

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/07.22.03.9448.01

Input Form

HypergeometricPFQ[{-(19/4)}, {3/2, -(9/4)}, z] == (1/(28194075 Sqrt[2])) (z^(1/4) ((28194075 + 75791520 z + 53786880 z^2 + 40550400 z^3 - 9846784 z^4 + 262144 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 8 Sqrt[z] (6493095 + 4102560 z + 2177280 z^2 - 605184 z^3 + 16384 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (45623655 + 91838880 z + 60560640 z^2 + 38191104 z^3 - 9781248 z^4 + 262144 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

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]