Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af3a)

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`=-9/2

http://functions.wolfram.com/07.22.03.af3a.01

Input Form

HypergeometricPFQ[{17/4}, {-(9/2), 23/4}, z] == -((209 (2 Sqrt[z] (213530411469375 + 240956840124000 z + 49692412224000 z^2 + 4451082854400 z^3 + 212027965440 z^4 + 5274337280 z^5 + 33554432 z^6) BesselI[-(1/4), Sqrt[z]]^2 - 17 (37681837318125 + 99941737896000 z + 32997549312000 z^2 + 4127193907200 z^3 + 260112384000 z^4 + 8996782080 z^5 + 134217728 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (640591234408125 + 332414910828000 z + 60049520294400 z^2 + 5071378636800 z^3 + 232656076800 z^4 + 5567938560 z^5 + 33554432 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(29444014080 Sqrt[2] z^(17/4)))

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]