Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af1u)

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`=-11/2

http://functions.wolfram.com/07.22.03.af1u.01

Input Form

HypergeometricPFQ[{17/4}, {-(11/2), 19/4}, z] == ((2 Sqrt[z] (14235360764625 + 16548794262000 z + 3883915526400 z^2 + 440108298240 z^3 + 33375191040 z^4 + 1601175552 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 - (42706082293875 + 114722317710000 z + 41327652038400 z^2 + 6149109657600 z^3 + 542218321920 z^4 + 33901510656 z^5 + 922746880 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (42706082293875 + 23616008816400 z + 4829699347200 z^2 + 519728025600 z^3 + 38091816960 z^4 + 1720713216 z^5 + 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (1840250880 Sqrt[2] z^(13/4))

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]