Q-analogue of summability of formal solutions of some linear q-difference-differential equations

Hidetoshi Tahara, Hiroshi Yamazawa

Research output: Contribution to journalArticle

8 Citations (Scopus)


Let q > 1. The paper considers a linear q-difference-differential equation: it is a q-difference equation in the time variable t, and a partial differential equation in the space variable z. Under suitable conditions and by using q-Borel and q-Laplace transforms (introduced by J.-P. Ramis and C. Zhang), the authors show that if it has a formal power series solution X(t; z ) one can construct an actual holomorphic solution which admits X(t; z ) as a q-Gevrey asymptotic expansion of order 1.

Original languageEnglish
Pages (from-to)713-738
Number of pages26
JournalOpuscula Mathematica
Issue number5
Publication statusPublished - 2015 Jan 1



  • Formal power series solutions
  • Q-Gevrey asymptotic expansions
  • Q-Laplace transform
  • Q-difference-differential equations
  • Summability

ASJC Scopus subject areas

  • Mathematics(all)

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