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

To compute some asymptotic expression I need to approximate $$\frac{(x-1)^{r+u}\left((x-1)^{p-r+1}+x^{p-r+1}\right)\left(x^{p-u+1}+(x-1)^{p+u+1}\right)}{\left(x^{2p+2}+(x-1)^{2p+2}\right)}$$ by some polynomial. Here $x\in(0,0.5)$,$p\geq r,u \geq 0$ some integers. Somehow Taylor and Lagrange methods don't work to me. What other methods should I try?

share|cite|improve this question
Have you tried multiplying out the numerator and using the binomial theorem? – Mose Wintner Apr 23 '11 at 15:19
up vote 2 down vote accepted

If you just tabulate the values for fixed $r,u$ at the proper points in (0,0.5) you can use a Chebyshev series, which is handy to give a bounded error. A description is available at Wikipedia (also see Chebyshev nodes) and at Numerical Recipes page 190, which includes C code.

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.