Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9762)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9762.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(9/2), 17/4}, z] == ((-2 Sqrt[z] (113437704805425 - 149623926051600 z + 3669032505600 z^2 + 18026366054400 z^3 + 3236880384000 z^4 + 247074914304 z^5 + 10519314432 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 + 3 (189062841342375 - 383817897262800 z + 26985313555200 z^2 + 21311678361600 z^3 + 3470362214400 z^4 + 256675676160 z^5 + 10754195456 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (567188524027125 + 58548492802800 z + 21478106707200 z^2 + 20735427686400 z^3 + 3433350758400 z^4 + 255228641280 z^5 + 10720641024 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(27467867750400 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]