Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I've been interested in series expansions of all types of mathematical functions. I was wondering if anyone has ever created a large list of all types of series. For example, Wolfram's Mathworld's Maclauren Series page list a bunch of those series. Herbert S. Wilf's Generatingfunctionology lists some power series at the end of section 2.5. Wikipedia lists some generalizations of series here and some Taylor series here.

I was wondering if there is a giant, somewhat comprehensive list of series somewhere. I'm especially interested in basic mathematical constants and elementary functions, but I'd like to have access to as many different series as possible. Could someone help me find some links or books with series?

Sorry if this seems hopelessly vague, but I would really like to have access to tons of series.

share|cite|improve this question
What do you want the series for? Anybody can come up with any crazy composition of functions, and that gives rise to a new series. – vonbrand Mar 6 '13 at 0:30
I'm really looking for series for elementary costants and functions to try to come up with new formulations and possibly closed forms of certain functions. For example, I'm studying the series $x+x^2+x^4+x^8+\dots+x^{2^n}+\dots$. I'm wondering if it's possible to find a closed form for the generating function. Mainly, I'd like to see various series for elementary functions and constants. I guess that currently I'm looking for series involving $e$, exponential series, and logarithm series. – Matt Groff Mar 6 '13 at 0:36
That series defines a lacunary function, it is even the first example given there. – vonbrand Mar 6 '13 at 0:40
@MattGroff: This seem like a Community Wiki type post. Would you like me to convert it to CW? – robjohn Mar 6 '13 at 0:53
@robjohn: Yes, if you don't mind. That would be excellent! Thanks! – Matt Groff Mar 6 '13 at 1:09

L B W Jolley, Summation of Series. Dover edition, published in 1961, is a revised and enlarged version of the 1925 original. "Over $1100$ common series are here collected, summed, and grouped for easy reference."

share|cite|improve this answer

There's a huge list (with summations near the bottom) of infinite series (although mostly infinite products here.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.