Аналитическая теория чисел, специальные функции, дзета-функция, математическая статистика, вариационное исчисление, история математики, приложения математики к инженерным дисциплинам, теория информации, теория сигнала, стохастическое кодирование, нейрокогнитивная робототехника.
Основные публикации:
F. Johansson and I. V. Blagouchine, “Computing Stieltjes constants using complex integration”, Mathematics of Computation, 88:318 (2019), 1829–1850
I. V. Blagouchine, “Three notes on Sers and Hasses representations for the zeta-functions”, Integers, 18A (2018), 1–45
I. V. Blagouchine, “Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to $\pi^{-1}$”, Journal of Mathematical Analysis and Applications, 442:2 (2016), 404–434
I. V. Blagouchine, “Rediscovery of Malmstens integrals, their evaluation by contour integration methods and some related results”, The Ramanujan Journal, 35:1 (2014), 21–110
I. V. Blagouchine and E. Moreau, “Unbiased Efficient Estimator of the Fourth-Order Cumulant for Random Zero-Mean non-i.i.d. Signal: Particular Case of MA Stochastic Process”, IEEE Transactions on Information Theory, 56:12 (2010), 6450–6458
I. V. Blagouchine, M.-A. Coppo, “A note on some constants related to the zeta-function and their relationship with the Gregory coefficients”, The Ramanujan Journal, 47:2 (2018), 457–473
I. V. Blagouchine, “Three notes on Ser's and Hasse's representations for the zeta-functions”, Integers, 18A (2018), #A3 , 45 pp. math.colgate.edu/~integers/sjs3/sjs3.pdf
6.
I. V. Blagouchine, “A note on some recent results for the Bernoulli numbers of the second kind”, Journal of Integer Sequences, 20:3 (2017), 17.3.8 , 7 pp.
7.
I. V. Blagouchine, “Addendum to Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results”, The Ramanujan Journal, 42:3 (2017), 777–781
8.
I. V. Blagouchine, “Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to $\pi^{-1}$”, Journal of Mathematical Analysis and Applications (Elsevier), 442:2 (2016), 404–434
I. V. Blagouchine, “A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments”, Journal of Number Theory (Elsevier), 148, 151 (2015), 537–592, 276–277
I. V. Blagouchine, “Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results”, The Ramanujan Journal (Springer), 35:1 (2014), 21–110
I. V. Blagouchine, E. Moreau, “Comments on ‘Unbiased estimates for moments and cumulants in linear regression’”, Journal of Statistical Planning and Inference (Elsevier), 142:4 (2012), 1027–1030
12.
I. V. Blagouchine, E. Moreau, “Analytic Method for the Computation of the Total Harmonic Distortion by the Cauchy Method of Residues”, IEEE Transactions on Communications, 59:9 (2011), 2478–2491
I. V. Blagouchine, E. Moreau, “Unbiased Efficient Estimator of the Fourth-Order Cumulant for Random Zero-Mean non-i.i.d. Signal: Particular Case of MA Stochastic Process”, IEEE Transactions on Information Theory, 56:12 (2010), 6450–6458
I. V. Blagouchine, E. Moreau, “Control of a Speech Robot via an Optimum Neural-Network-Based Internal Model with Constraints”, IEEE Transactions on Robotics, 56:1 (2010), 142–159
I. V. Blagouchine, E. Moreau, “Unbiased Adaptive Estimations of the Fourth-Order Cumulant for Real Random Zero-Mean Signal”, IEEE Transactions on Signal Processing, 57:9 (2009), 3330–3346
I. V. Blagouchine, A complement to a recent paper on some infinite sums with the zeta values, arXiv:2001.00108 [math.CA], arXiv, 2019 (Published online) , 4 pp. arxiv.org/abs/2001.00108
ArXiv
17.
Iaroslav V. Blagouchine, “Expansions of generalized Euler's constants into the series of polynomials in $\pi^{-2}$ and into the formal enveloping series with rational coefficients only”, Journal of Number Theory (Elsevier), 158,173 (2016), 365–396, 631–632
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