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Results tagged with special-functions
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user 36735
Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.
2
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Summation of certain series
Suppose $f(n)$ is a periodic function with period $q$. Now from this paper we get that if $\displaystyle\sum_{n=1}^{q}f(n)=0$ then $\displaystyle\sum_{n=1}^{\infty}\frac{f(n)}{n}=-\frac{1}{q}\displays …
- 1,692
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Accepted
Summation of certain series
Thanks to everyone whoever thought over this problem. I have asked Professor Murty (one of the authors of the paper mentioned in the question) about this question. He told me that, of course such gene …
- 1,692
1
vote
0
answers
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Kontorovich Lebedev transform
By the title I mean [reference: ``Spectral methods of Automorphic forms" by Iwaniec (B.41)-(B.43)] for $f\in C^\infty_c(\mathbb{R^+})$, one has
$$f(x)=\pi^{-2}\int_{-\infty}^\infty K_{it}(x)F_f(t)t\si …
- 1,692
5
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answer
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Asymptotic behaviour of $K$-Bessel function in transition range
It is known that the famous mistake of Iwaniec-Sarnak in their paper of $L^\infty$ norm of eigenfunction of non-cocompact arithmetic surfaces in lemma (A1) is because of they did not consider the bump …
- 1,692