Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7r6)

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`=3/2

http://functions.wolfram.com/07.22.03.a7r6.01

Input Form

HypergeometricPFQ[{-(17/4)}, {3/2, 17/4}, z] == ((2 Sqrt[z] (123743795175 - 345696951600 z + 30892689273600 z^2 - 56430433382400 z^3 + 19304635760640 z^4 - 1636417142784 z^5 + 40818966528 z^6 - 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 + 3 (-206239658625 + 722820898800 z - 1843717075200 z^2 + 41706988646400 z^3 - 17931283660800 z^4 + 1601096908800 z^5 - 40584085504 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-618718975875 + 848528881200 z - 3519823507200 z^2 + 43446224793600 z^3 - 18116694835200 z^4 + 1606067159040 z^5 - 40617639936 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(29899918540800 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]