Springer has just released a new textbook by Manuel Kauers about D-finite Functions.

Long text: Defined as solutions of linear differential or difference equations with polynomial coefficients, D-finite functions play an important role in various areas of mathematics. Kauers's new book "D-Finite Functions" is a comprehensive introduction to the theory of these functions with a special emphasis on computer algebra algorithms for computing with them: algorithms for detecting relations from given data, for evaluating D-finite functions, for executing closure properties, for obtaining various kinds of “explicit” expressions, for factoring operators, and for definite and indefinite symbolic summation and integration are covered.

The book is volume 30 in the Springer textbook series "Algorithms and Computation in Mathematics".