Some p-adic differential equations

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dc.creatorde Gosson, M.
dc.creatorDragovich, B.
dc.creatorKhrennikov, A.
dc.date2000-10-18
dc.date.accessioned2026-07-07T04:28:04Z
dc.date.available2026-07-07T04:28:04Z
dc.descriptionWe investigate various properties of p-adic differential equations which have as a solution an analytic function of the form $F_k (x) = \sum_{n\geq 0} n! P_k (n) x^n$, where $P_k (n) = n^k + C_{k-1} n^{k-1} + ...+ C_0$ is a polynomial in n with $C_i\in Z$ (in a more general case $C_i\in Q$ or $C_i\in C_p$). For some special classes of $P_k (n)$, as well as for the general case, the existence of the corresponding linear differential equations of the first- and second-order for $F_k (x)$, is shown. In some cases such equations are constructed. For the second-order differential equations there is no other analytic solution of the form $\sum a_n x^n$. Due to the fact that the corresponding inhomogeneous first-order differential equation exists one can construct infinitely many inhomogeneous second-order equations with the same analytic solution. Relation to some rational sums with the Bernoulli numbers and to $F_k (x)$ for some $x\in Z$ is considered. Some of these differential equations can be related to p-adic dynamics and p-adic information theory.
dc.description16 pages. Talk at VI Int. Conf. on p-Adic Functional Analysis, (Ioannina, 2000). To be publ. in Lecture Notes in Pure and Applied Mathematics
dc.identifierhttps://arxiv.org/abs/math-ph/0010023
dc.identifierhttp://arxiv.org/abs/math-ph/0010023
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56648
dc.subjectMathematical Physics
dc.titleSome p-adic differential equations
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