Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8du)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a8du.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(11/2), 17/4}, z] == ((-2 Sqrt[z] (5189960350575 - 6326808808320 z + 142435738368 z^2 + 277880537088 z^3 + 29528752128 z^4 + 1140850688 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (8649933917625 - 16695745466400 z - 771008958720 z^2 + 305512660992 z^3 + 30551769088 z^4 + 1155530752 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (25949801752875 + 5272340673600 z + 498888149760 z^2 + 301200703488 z^3 + 30400905216 z^4 + 1153433600 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (447624511488 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]