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I have never been good at solving recurrence relations. Part of the reason is that I have never found a book that is good at explaining the strategies for solving them; The books just give formulas for solving recurrence relations of specific forms.

So, what books do you recommend to learn how to solve recurrence relations?

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    $\begingroup$ Personally, I would suggest that if you search the recurrence relations tag on this site you will find more material on theory and practical problem solving than in most books. And if there is something you don't understand it is easy to ask for clarification. $\endgroup$
    – Mark Bennet
    Aug 7, 2015 at 21:21
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    $\begingroup$ generatingfunctionology by Wilf. definitely. $\endgroup$
    – gogurt
    Aug 7, 2015 at 21:22
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    $\begingroup$ @gogurt: Yes, but that might be a bit demanding for a start; if so, the relevant parts of Graham, Knuth, and Patashnik, Concrete Mathematics, are an excellent introduction and preparation for Wilf. And Mark Bennet's suggestion is a very good one. $\endgroup$
    – Brian M. Scott
    Aug 7, 2015 at 21:32
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    $\begingroup$ @MarkBennet And if you search the entire internet you'll find even more than you can find here ;) when I buy a book I'm paying for entropy. The stuff here is usually too fragmented to use in any attempt to learn a subject. I use this site mostly as a refresher, supplement, and entertainment source, not as a collection of the most relevant material on the subject I'm interested in. $\endgroup$
    – Zach466920
    Aug 7, 2015 at 21:43
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    $\begingroup$ @Ovi: It has a couple of rough spots, but overall I think that it’s one of the best-written textbooks I’ve encountered in my entire career as student and teacher. You’re welcome! $\endgroup$
    – Brian M. Scott
    Dec 31, 2016 at 23:05

2 Answers 2

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Here I'd like to draw attention to The Concrete Tetrahedron by M. Kauers and P. Paule. This book puts the focus on four strongly connected types of mathematical objects

  • recurrences

  • generating functions

  • symbolic sums

  • asymptotic estimations

and the interplay between them. The connections and structural properties of these four regions are analysed starting with polynomials as the most simple application and going step by step, i.e. chapter by chapter to more complex objects. The authors cover

and in each of these chapters the four regions and their interplay is discussed.

Btw. the term Concrete in the title of the book is a reverence to Concrete Mathematics by R. L. Graham, D. Knuth and O. Patashnik which is explicitly stated by the authors in section 1.6:

  • The attribute concrete is a reference to the book "Concrete Mathematics" by Graham, Knuth, and Patashnik [24], where a comprehensive introduction to the subject is provided. Following the authors of that book, we understand concrete not in contrast to abstract, but as a blend of the two words con-tinuous and dis-crete, for it is both continuous and discrete mathematics that is applied when solving concrete problems.
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  • $\begingroup$ @HernánEche: Many thanks for granting the bounty! :-) $\endgroup$
    – epi163sqrt
    Jul 21, 2021 at 18:43
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RECURRENCE AND TOPOLOGY, John M. Alongi, Gail S. Nelson, Graduate Studies in Mathematics,Volume 85, American Mathematical Society. Providence, Rhode Island. Publication Year: 2007 ISBN-10: 0-8218-4234-X ISBN-13: 978-0-8218-4234-8 www.ams.org/bookpages/gsm-85

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