On one integral representation of Binet type
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 741-754 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present work, we obtain a generalization of the classical Binet formula. It is used to find a functional relationship for the Riemann zeta-function. We obtain the mentioned generalization by means of the Plan formula.
Mots-clés : Binet formula
Keywords: integral representation, entire function.
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V. I. Kuzovatov; A. M. Kytmanov. On one integral representation of Binet type. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 741-754. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a56/

[1] E.T. Whittaker, G.N. Watson, A course of modern analysis, Cambridge University Press, Cambridge, 1927 | MR | Zbl

[2] E.C. Titchmarsh, The theory of the Riemann zeta-function, Clarendon Press, Oxford, 1951 | MR | Zbl

[3] I.M. Gel'fand, B.M. Levitan, “On a simple identity for the eigenvalues of a second-order differential operator”, Dokl. Akad. Nauk SSSR, n. Ser., 88:4 (1953), 593–596 | MR | Zbl

[4] L.A. Dikii, “The zeta-function of an ordinary differential equation on a finite interval”, Izv. Akad. Nauk SSSR Ser. Mat., 19:4 (1955), 187–200 | MR | Zbl

[5] L.A. Dikii, “Trace formulas for Sturm-Liouville differential operators”, Usp. Mat. Nauk, 13:3 (1958), 111–143 | MR | Zbl

[6] V.B. Lidskii, V.A. Sadovnichii, “Regularized sums of zeros of a class of entire functions”, Funkts. Anal. Prilozh., 1:2 (1967), 133–139 | DOI | MR | Zbl

[7] S.A. Smagin, M.A. Shubin, “On the zeta function of a transversally elliptic operator”, Russ. Math. Surv., 39:2 (1984), 201–202 | DOI | MR | Zbl

[8] A.M. Kytmanov, S.G. Myslivets, “On the zeta-function of systems of nonlinear equations”, Sib. Math. J., 48:5 (2007), 863–870 | DOI | MR | Zbl

[9] V.I. Kuzovatov, A.A. Kytmanov, “On the zeta-function of zeros of some class of entire functions”, J. Sib. Fed. Univ., Math. Phys., 7:4 (2014), 489–499 | DOI | Zbl

[10] A.B. Kostin, V.B. Sherstyukov, “Integral representations of quantities associated with gamma function”, Ufa Math. J., 13:4 (2021), 50–62 | DOI | MR | Zbl

[11] A.I. Markushevich, The theory of analytic functions, v. 2, Nauka, M., 1968 | MR | Zbl

[12] E.C. Titchmarsh, The theory of functions, Oxford University Press, Oxford, 1939 | MR | Zbl

[13] V.I. Kuzovatov, A.M. Kytmanov, A. Sadullaev, “On the zeta-function of zeros of an entire function”, J. Sib. Fed. Univ., Math. Phys., 14:5 (2021), 599–603 | DOI | MR | Zbl

[14] V.I. Kuzovatov, A.M. Kytmanov, “On an analog of the Binet integral representation”, Sib. Èlektron. Mat. Izv., 17 (2020), 840–852 | DOI | MR | Zbl

[15] V.I. Kuzovatov, “Generalization of Plan's formula”, Russ. Math., 62:5 (2018), 34–43 | DOI | Zbl

[16] H. Bateman, A. Erdelyi, Higher transcendental functions, v. 1, MC Graw-Hill Book Company, New York etc., 1953 | MR

[17] B.Ja. Levin, Distribution of zeros of entire functions, American Mathematical Society, Providence, 1980 | MR