Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af0q)

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.af0q.01

Input Form

HypergeometricPFQ[{17/4}, {-(11/2), -(21/4)}, z] == (1/(1270002108375 Sqrt[2])) (z^(1/4) ((1270002108375 + 2726930934000 z + 1923512572800 z^2 + 543732134400 z^3 + 102758423040 z^4 + 19725189120 z^5 + 22543073280 z^6 + 9294577664 z^7 + 33554432 z^8) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-1270002108375 - 1710929247300 z - 645080436000 z^2 - 138218633280 z^3 - 24505528320 z^4 - 6038323200 z^5 + 14917042176 z^6 + 482344960 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (1270002108375 + 694927560600 z + 179449648560 z^2 + 32960753280 z^3 + 6239600640 z^4 + 2415329280 z^5 + 2205155328 z^6 + 8388608 z^7) 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]