Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9n6)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a9n6.01

Input Form

HypergeometricPFQ[{-(9/4)}, {9/2, 17/4}, z] == -((13 (2 Sqrt[z] (-613253025 - 941537520 z - 1720502784 z^2 + 1045389312 z^3 - 75300864 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]]^2 + 3 (1022088375 + 1321412400 z + 910103040 z^2 - 981049344 z^3 + 74383360 z^4 - 1048576 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (1270009125 + 1404572400 z + 1007424000 z^2 - 989945856 z^3 + 74514432 z^4 - 1048576 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(13644804096 Sqrt[2] z^(11/4)))

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]