Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

There is a function I met in complex analysis. $$f(\lambda) = \int \limits_{-\infty}^{\infty}\frac{e^{i\lambda x}}{\sqrt{1 + x^{2n}}}dx$$

share|improve this question
1  
Maple does something complicated in terms of the Meijer G function. –  GEdgar Dec 16 '12 at 14:23
    
I read about McDonalds function, $$ f(\lambda ) = \int \limits_{-\infty}^{\infty} \frac{e^{i \lambda x}dx}{\sqrt{1 + x^2}}. $$ It's one of the Bessel's function. Has the function from my question the name as the, maybe, Bessel's function? –  John Taylor Dec 16 '12 at 15:00
add comment

1 Answer

It's called the Fourier Transform of $\frac1{\sqrt{1+x^{2n}}}$.

share|improve this answer
    
I read about McDonald function, $$ f( \lambda ) = \int \limits_{-\infty}^{\infty}\frac{e^{i \lambda x}dx}{\sqrt{1 + x^2}}. $$ It's one of Bessel's function. Has the function from my question the name as the Bessel's function? –  John Taylor Dec 16 '12 at 14:52
    
@Maxim_Ovchinnikov sorry I don' t know, but if I'll ever find something I'll let you know... –  draks ... Dec 19 '12 at 10:52
add comment

Your Answer

 
discard

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.