Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aen8)

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`=-9/2

http://functions.wolfram.com/07.22.03.aen8.01

Input Form

HypergeometricPFQ[{15/4}, {-(9/2), 21/4}, z] == -((221 (-6 Sqrt[z] (-1729986783525 + 1568183379840 z + 446557224960 z^2 + 44341592064 z^3 + 2133327872 z^4 + 41943040 z^5) BesselI[1/4, Sqrt[z]]^2 + (-25949801752875 + 41975943055200 z + 17729717322240 z^2 + 2369234165760 z^3 + 149594701824 z^4 + 4586471424 z^5 + 33554432 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 6 Sqrt[z] (8649933917625 + 4461211339200 z + 795430056960 z^2 + 65190051840 z^3 + 2741764096 z^4 + 46137344 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(5086642176 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]