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Onq-difference equations andZ n decompositions of exp q function

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Abstract

Theq-extended hyperbolic functions ofn-th order {h q,s(z)}s∈ Z n which areZ n-components of expq function form the set fundamental solutions of a simpleq-difference equation. Against the background ofq-deformed hyperbolic functions ofn-th order other natural extensions and related topics are considered. Apart from easy general solution of homogenous ordinaryq-difference equations ofn-th order main trigonometric-like identity known for hyperbolic functions ofn-th order is given itsq-commutative counterpart. Hint how to arrive at other identities is implicit in theq-treatment proposed. The paper constitutes an example of the application of the method of projections presented in Advances in Applied Clifford Algebras publication [19]; see also references to Ben Cheikh’s papers.

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Authors and Affiliations

  1. Institute of Computer Science, Bialystok University, ul. Sosnowa 64, PL-15-887, Bialystok, Poland

    A. K. Kwaśniewski

  2. Institute of Mathematics, Bialystok University (student), Bialystok, Poland

    B. K. Kwaśniewski

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Kwaśniewski, A.K., Kwaśniewski, B.K. Onq-difference equations andZ n decompositions of exp q function. AACA 11, 39–61 (2001). https://doi.org/10.1007/BF03042038

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