Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af62)

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`=-3/2

http://functions.wolfram.com/07.22.03.af62.01

Input Form

HypergeometricPFQ[{17/4}, {-(3/2), -(21/4)}, z] == (1/(366522975 Sqrt[2])) (z^(1/4) ((366522975 + 930852000 z + 1079788320 z^2 + 488816640 z^3 - 780910592 z^4 + 201850880 z^5 + 2097152 z^6) BesselI[-(1/4), Sqrt[z]]^ 2 + 4 Sqrt[z] (-366522975 - 637633620 z - 595745280 z^2 + 443111424 z^3 + 11927552 z^4 + 19660800 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (366522975 + 344415240 z - 26823168 z^2 - 188461056 z^3 + 45678592 z^4 + 524288 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]