Symbolic integration of expressions involving unspecified functions
ACM SIGSAM Bulletin
Integration of rational functions: Rational computation of the logarithmic part
Journal of Symbolic Computation
The method of differentiating under the integral sign
Journal of Symbolic Computation
A note on Gro¨bner bases and integration of rational functions
Journal of Symbolic Computation
Symbolic integration I: transcendental functions
Symbolic integration I: transcendental functions
Application of unspecified sequences in symbolic summation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
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An algorithm for parametric elementary integration over differential fields constructed by a differentially transcendental extension is given. It extends current versions of Risch's algorithm to this setting and is based on some first ideas of Graham H. Campbell transferring his method to more formal grounds and making it parametric, which allows to compute relations among definite integrals. Apart from differentially transcendental functions, such as the gamma function or the zeta function, also unspecified functions and certain families of iterated integrals such as the polylogarithms can be modeled in such differential fields.