Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af0y)

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.af0y.01

Input Form

HypergeometricPFQ[{17/4}, {-(11/2), -(13/4)}, z] == (1/(3557428875 Sqrt[2])) (z^(1/4) ((3557428875 + 7960680000 z + 6179846400 z^2 + 2295820800 z^3 + 1012677120 z^4 - 362127360 z^5 + 392560640 z^6 + 2097152 z^7) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-3557428875 - 5114736900 z - 2341029600 z^2 - 755576640 z^3 - 266757120 z^4 + 404766720 z^5 + 25427968 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (3557428875 + 2268793800 z + 778967280 z^2 + 262604160 z^3 - 170956800 z^4 + 91914240 z^5 + 524288 z^6) 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]