<p>Integral representations of two <i>q</i>-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to <i>q</i>-difference equations in the complex domain. Both representations are unified through the so-called (<i>p</i>,&#xa0;<i>q</i>)-differential operator, for which a kernel-like function is provided, generating the sequence of (<i>p</i>,&#xa0;<i>q</i>)-factorials.</p>

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On integral representations of q-difference operators and their applications

  • Antonio Cáceres,
  • Alberto Lastra,
  • Sławomir Michalik,
  • Maria Suwińska

摘要

Integral representations of two q-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to q-difference equations in the complex domain. Both representations are unified through the so-called (pq)-differential operator, for which a kernel-like function is provided, generating the sequence of (pq)-factorials.