Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ada2)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.ada2.01

Input Form

HypergeometricPFQ[{9/4}, {-(9/2), -(21/4)}, z] == -((1/(986792625 Sqrt[2])) (z^(1/4) (5 (-197358525 - 413513100 z - 276475680 z^2 - 67953600 z^3 - 10681344 z^4 - 1916928 z^5 + 1835008 z^6) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (986792625 + 1278131400 z + 430045200 z^2 + 77984640 z^3 + 11520000 z^4 + 3440640 z^5 + 524288 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 12 z (-328930875 - 162899100 z - 36419760 z^2 - 5564160 z^3 - 921600 z^4 + 720896 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2))

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]