Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8c4)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8c4.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 3/4}, z] == ((4 z (-14707625625 + 5042614500 z - 2724321600 z^2 + 38284646400 z^3 - 63581414400 z^4 + 11388764160 z^5 - 454819840 z^6 + 4194304 z^7) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-44122876875 + 6723486000 z - 4854880800 z^2 + 6519744000 z^3 - 28589299200 z^4 + 5555773440 z^5 - 226099200 z^6 + 2097152 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (132368630625 + 5042614500 z + 9412880400 z^2 - 16485638400 z^3 + 104315904000 z^4 - 243616665600 z^5 + 45106790400 z^6 - 1815085056 z^7 + 16777216 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(142125984000 Sqrt[2] z^(15/4))

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]