Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8320)

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`=3/2

http://functions.wolfram.com/07.22.03.8320.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 15/4}, z] == ((2 Sqrt[z] (276704875321875 - 758961943740000 z + 122431033932480000 z^2 - 191904063173222400 z^3 + 52703425010073600 z^4 - 4255570250956800 z^5 + 122894617149440 z^6 - 1312649379840 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 + (-830114625965625 + 1011949258320000 z - 56669158465920000 z^2 + 164872944952934400 z^3 - 50235518140416000 z^4 + 4180915991347200 z^5 - 122081425489920 z^6 + 1309965025280 z^7 - 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-830114625965625 + 2782860460380000 z + 89105505359270400 z^2 - 180187366767206400 z^3 + 51685201870848000 z^4 - 4225351444070400 z^5 + 122568132526080 z^6 - 1311575638016 z^7 + 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(204173822361600000 Sqrt[2] z^(9/4))

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]