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- W2043867329 abstract "This paper is concerned with the integro-differential equationsy′(t)=ay(t)+∫01y(qt)dμ(q)+∫01y′(qt)dν(q)andy(t)+∫01y(qt)dμ(q)+∫01y′(qt)dν(q)=0,whereais a complex constant, and μ and ν are complex-valued functions of bounded variation on [0, 1]. The main motivation is that the generalized hypergeometric functionAFB(α1,…,αA; β1,…,βB; t) satisfies the first equation whenA ≤ Band the second equation whenA = B + 1 for appropriately chosen constantaand smooth functions μ and ν. The first equation also includes as a special case the well-known pantograph equation and many of its generalisations. The main objects of this paper are well-posedness of initial value problems, Dirichlet and Dirichlet–Taylor series expansions, and asymptotic behaviour of the solutions." @default.
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- W2043867329 date "1997-04-01" @default.
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- W2043867329 title "Integro-differential Equations and Generalized Hypergeometric Functions" @default.
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- W2043867329 doi "https://doi.org/10.1006/jmaa.1997.5322" @default.
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