Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9548)

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`=7/2

http://functions.wolfram.com/07.22.03.9548.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, -(5/4)}, z] == -(((4 z (1140591375 - 4172464800 z - 6385132800 z^2 - 8099020800 z^3 + 3201556480 z^4 - 180879360 z^5 + 2097152 z^6) BesselI[-(1/4), Sqrt[z]]^ 2 - 4 Sqrt[z] (3421774125 - 2780870400 z - 3923136000 z^2 - 3188736000 z^3 + 1546014720 z^4 - 89784320 z^5 + 1048576 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (10265322375 - 6387311700 z + 22878979200 z^2 + 29812608000 z^3 + 29461708800 z^4 - 12628623360 z^5 + 721420288 z^6 - 8388608 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(12113010000 Sqrt[2] z^(7/4)))

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]