Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8380)

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`=7/2

http://functions.wolfram.com/07.22.03.8380.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(21/4)}, z] == ((4 z (-639695882184975 + 549479043867600 z + 264360787257600 z^2 + 40031725916160 z^3 + 3184639672320 z^4 + 163398549504 z^5 + 6325010432 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-1919087646554925 + 448081908258600 z + 149269492310400 z^2 + 21206033418240 z^3 + 1650255298560 z^4 + 83901284352 z^5 + 3246391296 z^6 + 134217728 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (5757262939664775 - 247624212458700 z + 2578436244014400 z^2 + 1104479494272000 z^3 + 163633442734080 z^4 + 12913816633344 z^5 + 660338638848 z^6 + 25568477184 z^7 + 1073741824 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (1113086292318000 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]