Analytic Coefficients Research Articles

Expansion problems in connection with homogeneous linear 𝑞-difference equations

1. Statement of the problem. This paper has for its purpose the development of expansion theories for the general homogeneous linear qdifference equation with analytic coefficients analogous to those of Neumann and Gegenbauer for Bessel's equation.t In Part II is treated the expansion of an arbitrary analytic function of a single variable in series analogous to those of Maclaurin and Laurent. In Part III expansions of functions of several variables are considered.