Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8460)

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/07.22.03.8460.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 11/4}, z] == ((2 z (491093022420000 + 11047985259436125 z + 123398950755366000 z^2 - 86461489717574400 z^3 + 13247310867148800 z^4 - 681864870297600 z^5 + 13654394142720 z^6 - 107122524160 z^7 + 268435456 z^8) BesselI[-(1/4), Sqrt[z]]^2 - Sqrt[z] (2946558134520000 + 26857965091332375 z + 85473358688718000 z^2 - 79184195126150400 z^3 + 12842876151705600 z^4 - 673507683532800 z^5 + 13587893452800 z^6 - 106954752000 z^7 + 268435456 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 (-1104959300445000 + 4714493015232000 z + 23429960404475625 z^2 + 105924768161612400 z^3 - 83392788662726400 z^4 + 13081986208051200 z^5 - 678492622356480 z^6 + 13627718369280 z^7 - 107055415296 z^8 + 268435456 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(174031643111040000 Sqrt[2] z^(11/4))

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]