Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9934)

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`=-1/2

http://functions.wolfram.com/07.22.03.9934.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(1/2), -(3/4)}, z] == (1/(10395 z^(1/4))) (Sqrt[2] ((10395 - 138600 z + 1774080 z^2 - 2350656 z^3 + 489472 z^4 - 16384 z^5) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (3465 - 41580 z + 243320 z^2 - 59392 z^3 + 2048 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (10395 - 110880 z + 499920 z^2 - 119296 z^3 + 4096 z^4) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]