Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8128)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.8128.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 15/4}, z] == -(((2 Sqrt[z] (99613755115875 + 21684626964000 z - 183232230105600 z^2 - 159340782182400 z^3 - 58919701708800 z^4 - 22915087073280 z^5 + 10589275422720 z^6 - 472983273472 z^7 + 4294967296 z^8) BesselI[-(1/4), Sqrt[z]]^2 + (-298841265347625 - 520431047136000 z + 138781612569600 z^2 + 170562790195200 z^3 + 60286884249600 z^4 + 17041289379840 z^5 - 10300875079680 z^6 + 470298918912 z^7 - 4294967296 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (298841265347625 - 117096985605600 z + 208172418854400 z^2 + 170930812723200 z^3 + 61302649651200 z^4 + 20444621045760 z^5 - 10472707325952 z^6 + 471909531648 z^7 - 4294967296 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(422337576960000 Sqrt[2] z^(9/4)))

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]