Geodesic
On a Ramanujan Identity and Its Generalizations
Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 524-536

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present paper, we propose a new method of derivation of number-theoretic identities which is applied to the proof of the multidimensional analogue of one of the Ramanujan identities. This method allows us to obtain new infinite series representations for the number $\pi$, of the values of the Riemann zeta function, and of the $L$-Dirichlet series at integer points.
Keywords: Ramanujan identity, hyperbolic functions, Dirichlet character modulo $4$. 
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     author = {A. T. Daniyarkhodzhaev and M. A. Korolev},
     title = {On a {Ramanujan} {Identity} and {Its} {Generalizations}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a3/}
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A. T. Daniyarkhodzhaev; M. A. Korolev. On a Ramanujan Identity and Its Generalizations. Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 524-536. http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a3/