Geodesic
Integer sequences connected to the Laplace continued fraction and Ramanujan's identity
Journal of integer sequences, Tome 19 (2016) no. 6
We consider integer sequences connected to the famous Laplace continued fraction for the function $R(t)=\int_t^\infty\varphi(x) \mathrm{d}x/\varphi(t)$, where $\varphi(t) = e^{-t^2/2}/\sqrt{2\pi}$ is the standard normal density. We compute the generating functions for these sequences and study their relation to the Hermite and Bessel polynomials. Using the master equation for the generating functions, we find a new proof of the Ramanujan identity.
Classification : 11Y05, 11Y55
Keywords: continued fraction, integer sequence, Ramanujan identity 
@article{JIS_2016__19_6_a2,
     author = {Kreinin,  Alexander},
     title = {Integer sequences connected to the {Laplace} continued fraction and {Ramanujan's} identity},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {6},
     zbl = {1417.11005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_6_a2/}
}
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Kreinin,  Alexander. Integer sequences connected to the Laplace continued fraction and Ramanujan's identity. Journal of integer sequences, Tome 19 (2016) no. 6. http://geodesic.mathdoc.fr/item/JIS_2016__19_6_a2/