together with their Maple implementations, which is relevant both to people being interested in symbolic computation and in q-series. For all these algorithms, the theoretical background is alreadyâ€¦ (More)

complex analysis. In some Computer Algebra Systems (CASs) it is possible to define an FPS by direct or recursive definition of its coefficients. Since some operations cannot be directly supportedâ€¦ (More)

Formal Laurent-Puisieux series (LPS) of the form [EQUATION] are important in calculus and complex analysis. In some Computer Algebra Systems (CASs) it is possible to define an LPS by direct orâ€¦ (More)

k = 0 sponding analytic functions. Since a goal of Computer Algebra is to work with formal objects and preserve such symbolic information, it should be possible to automate conversion between theseâ€¦ (More)

Let us consider the differential equation Ïƒ(x)y â€²â€² n(x) + Ï„(x)y â€² n(x) âˆ’ Î»nyn(x) = 0 (1) and search for its polynomial solutions in form Pn(x) = knx + knâˆ’1xnâˆ’1 + Â· Â· Â· We will often consider theâ€¦ (More)

In [6]â€“[9] the first author published an algorithm for the conversion of analytic functions for which derivative rules are given into their representing power series âˆž âˆ‘ k=0 akz k at the origin andâ€¦ (More)

For differential operators of order 2, this paper presents a new method that combines generalized exponents to find those solutions that can be represented in terms of Bessel functions.

The celebrated Zeilberger algorithm which finds holonomic recurrence equations for definite sums of hypergeometric terms F (n, k) is extended to certain nonhypergeometric terms. An expression F (n,â€¦ (More)

Studentâ€™s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samplesâ€¦ (More)