Research Interests

• Special functions;
• Neumann, Kapteyn and Schlomilch series;
• Integral representations; Summation formulas; Application in Probability Theory

Degrees

• PhD in Mathematical Analysis, Department of Mathematics, University of Zagreb, 2011.
• BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2007.

Publications

1. D. Jankov Maširević, T. Poganj, T. Burić, Integral and series representations of the Nuttall function, Journal of Computational and Applied Mathematics 453 (2025), 1-11
   Abstract

   In this paper we obtain two new integral representation formulae for the Nuttall function; the first one is a linear combination of the confluent hypergeometric function (Kummer function) and a Laplace–Mellin transform of a product of the Bessel function of the first kind and a generalized hypergeometric function , whilst the second representation is a linear combination built of the Kummer function and a Grünwald–Letnikov fractional derivative of the Kampé de Fériet double hypergeometric function. The latter we derive as a by-product of the Grünwald–Letnikov fractional derivative of the Kampé de Fériet function obtained for the incomplete Toronto function . New series representation is established for the Nuttall function whose building blocks are generalized hypergeometric functions. Also a simple connection formula between Nuttall and Marcum –function is presented. Finally, we give the closed form formula for the Nuttall function in terms of upper incomplete gamma function which also simplifies some already known results. In addition, a section devoted to the computational efficiency of the newly derived formulae versus already known formulae is exposed.
2. K. Gorska, A. Horzela, D. Jankov Maširević, T. Poganj, On Distribution of Rice–Middleton Model, Results in Mathematics 79 (2024)
3. D. Jankov Maširević, The McKay $I_nu$ Bessel distribution revisited, Fractional Calculus and Applied Analysis (2024), 1-18
   Abstract

   Bearing in mind an increasing popularity of the fractional calculus the main aim of this paper is to derive several new representation formulae for the cumulative distribution function (cdf) of the McKay $I_\nu$ Bessel distribution including the Grünwald-Letnikov fractional derivative; also, two connection formulae between cdf of the McKay $I_\nu$ random variable and the so–called Neumann series of modified Bessel functions of the first kind are established, providing, consequently, a new integral representation for such cdf in terms of a definite integral. Another fashion expression for the given cdf is derived in terms of the Grünwald-Letnikov fractional derivative of the widely applicable Marcum Q–function, which represents a certain simplification of the already existing relationship between McKay $I_\nu$ random variable and a Marcum Q–functions. The exposition ends with some open questions, drawing the interested reader’s attention, among others, to the summation of some Neumann series.
4. D. Jankov Maširević, T. Poganj, Bounds for confluent Horn function Φ2 deduced by McKay Iν Bessel law, Rad HAZU, Matematičke znanosti. 27 (2023), 123-131
5. D. Jankov Maširević, T. Poganj, Functional bounds for Exton's double hypergeometric X function, Journal of Mathematical Inequalities 17/1 (2023), 259-267
6. Y. A. Brychkov, D. Jankov Maširević, T. Poganj, New expression for CDF of $\chi_n'^{\;2}(\lambda)$ distribution and Marcum Q_1 function, Results in Mathematics 77/102 (2022)
7. K. Gorska, A. Horzela, D. Jankov Maširević, T. Poganj, Observations on the McKay Iν Bessel distribution, Journal of Mathematical Analysis and Applications 516/1 (2022)
8. A. Baricz, D. Jankov Maširević, T. Poganj, Approximation of CDF of non-central chi-square distribution by mean-value theorems for integrals, Mathematics 9/2 (2021)
9. D. Jankov Maširević, T. Poganj, CDF of non-central χ2 distribution revisited. Incomplete hypergeometric type functions approach, Indagationes Mathematicae 32/4 (2021), 901-915
10. D. Jankov Maširević, T. Poganj, On a second type Neumann series of modified Bessel functions of the first kind, Integral Transforms and Special Functions (2020), prihvaćen za objavljivanje
11. D. Jankov Maširević, T. Poganj, Second Type Neumann Series of Generalized Nicholson Function, Results in Mathematics 75/12 (2020)
12. D. Jankov Maširević, T. Poganj, Integral Representations for Products of Two Bessel or Modified Bessel Functions, Mathematics 7/10 (2019)
13. D. Jankov Maširević, T. Poganj, On new formulae for cumulative distribution function for McKay Bessel distribution, Communications in Statistics - Theory and Methods (2019), prihvaćen za objavljivanje
14. D. Jankov Maširević, T. Poganj, On series representations for modified Bessel function of second kind of integer order, Integral Transforms and Special Functions 30/3 (2019), 181-189
15. D. Jankov Maširević, Summations of Schlomilch series containing Anger function terms, Mathematica Slovaca 68/1 (2018), 103-114
16. D. Jankov Maširević, R.K. Parmar , T. Poganj, (p, q)-Extended Bessel and Modified Bessel Functions of the First Kind, Results in Mathematics 72 (2017), 617-632
17. D. Jankov Maširević, T. Poganj, Infinite summations of hypergeometric type terms by a probabilistic method, The Journal of Analysis 25/1 (2017), 83-92
18. D. Jankov Maširević, On New Formulas for the Cumulative Distribution Function of the Noncentral Chi-Square Distribution, Mediterranean Journal of Mathematics 14/66 (2017)
19. D. Jankov Maširević, T. Poganj, p -Extended Mathieu Series from the Schlömilch Series Point of View, Vietnam Journal of Mathematics 45/4 (2017), 713-719
20. A. Baricz, S. Ponnusamy, S. Singh, D. Jankov Maširević, Bounds for the product of modified Bessel functions, Aequationes mathematicae 90/4 (2016), 859-870
21. D. Jankov Maširević, Summations of Schlomilch series containing some Lommel functions of the first kind terms, Integral Transforms and Special Functions 27/2 (2016), 153-162
22. D. Jankov Maširević, Summations of Schlömilch series containing Struve function terms, Georgian Mathematical Journal 23/3 (2016), 363-366
23. D. Jankov Maširević, S. Miodragović, Geometric median in the plane, Elemente der Mathematik 70 (2015), 21-32
24. D. Jankov Maširević, T. Poganj, New summations of Neumann series of modified Bessel functions, The Journal of Analysis 23 (2015), 47-57
25. A. Baricz, D. Jankov Maširević, T. Poganj, R. Szasz, On an identity for zeros of Bessel functions, Journal of Mathematical Analysis and Applications 422/1 (2015), 27-36
26. D. Jankov Maširević, Sturm-Liouville problem and I-Bessel sampling, Acta Polytechnica Hungarica 12/2 (2015), 231-246
27. D. Jankov Maširević, Summations of Schlömilch series containing modified Bessel function of the second kind terms, Integral Transforms and Special Functions 26/4 (2015), 273-281
28. D. Jankov Maširević, T. Poganj, Bounds on Čebyšev functional for C_φ[0,1] function class, The Journal of Analysis 22 (2014), 107-117
29. D. Jankov Maširević, T. Poganj, On coefficients of Kapteyn-type series, Mathematica Slovaca 65/2 (2014), 403-410
30. D. Jankov Maširević, T. Poganj, Bounds on weighted discrete Čebyšev functional, ProbStat Forum 6 (2013), 1-9
31. A. Baricz, D. Jankov Maširević, T. Poganj, Integral representations of Dini series of Bessel functions, Integral Transforms and Special Functions 24/8 (2013), 628-635
32. D. Jankov Maširević, T. Poganj, Andreev-Korkin identity, Saigo fractional integration operator and $Lip_L(α)$ functions, Journal of Mathematical Physics, Analysis and Geometry 8/2 (2012), 144-157
33. D. Jankov Maširević, T. Poganj, Integral representation of functional series with members containing Jacobi polynomials, Mathematica Balkanica 26/1-2 (2012), 103-112
34. D. Jankov Maširević, T. Poganj, Integral representation of Schlömilch series, Journal of Classical Analysis 1/1 (2012), 75-84
35. D. Jankov Maširević, A. Baricz, T. Poganj, Integral representations for Neumann-type series of Bessel functions $I_nu, $ $Y_nu$ and $K_nu$, Proceedings of the American Mathematical Society 140/3 (2012), 951-960
    Abstract

    Recently Pog'any and S"uli [Proc. Amer. Math. Soc. 137(7)(2009), 2363-2368] derived a closed-form integral expression for Neumann series of Bessel functions of the first kind $J_nu$. In this note our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind $I_nu$, for Bessel functions of the second kind $Y_nu, K_nu$ and to give links for the same question for the Hankel functions $H_nu^(1) ; H_nu^(2)$.
36. A. Baricz, D. Jankov Maširević, T. Poganj, Neumann series of Bessel functions, Integral Transforms and Special Functions 23/7 (2012), 529-538
37. A. Baricz, D. Jankov Maširević, T. Poganj, Turán type inequalities for Krätzel functions, Journal of Mathematical Analysis and Applications 388/2 (2012), 716-724
38. D. Jankov Maširević, T. Poganj, R.K. Saxena, Extended general Hurwitz-Lerch Zeta function as Mathieu (a, lambda) - series, Applied mathematics letters 24/8 (2011), 1473-1476
39. A. Baricz, D. Jankov Maširević, T. Poganj, Integral representation of first kind Kapteyn series, Journal of mathematical physics 52/4 (2011)
    Abstract

    The main aim of this research note is to establish two different types of integral representation formulae for the Kapteyn series of the first kind. The first one is a double definite integral expression, while the second type includes indefinite integral representation formula.
40. R.K. Saxena, T. Poganj, R. Saxena, D. Jankov Maširević, On generalized Hurwitz-Lerch Zeta distributions occuring in statistical inference, Acta Universitatis Sapientiae Mathematica 3/1 (2011), 43-59
41. D. Jankov Maširević, T. Poganj, E. Suli, On the coefficients of Neumann series of Bessel functions, Journal of Mathematical Analysis and Applications 380/2 (2011), 628-631
42. H.M. Srivastava, D. Jankov Maširević, T. Poganj, R.K. Saxena, Two-Sided Inequalities for the Extended Hurwitz-Lerch Zeta Function, Computers & Mathematics with Applications 62/1 (2011), 516-522

1. D. Jankov Maširević, T. Poganj, A. Baricz, A. Galántai, Sampling Bessel functions and Bessel sampling, 8th International Symposium on Applied Computational Intelligence and Informatics, Timisoara, Romania, 2013, 79-84
2. M. Benšić, D. Jankov Maširević, Parameter estimation for a three-parameter Weibull distribution - a comparative study, 12th International Conference on Operational Research, Pula, Croatia, 2008, 159-164

1. D. Jankov Maširević, M. Mikić, Kombinatorika i vjerojatnost – zajedno kroz ples, Osječki matematički list 19/2 (2019), 123-136
2. D. Jankov Maširević, N. Keglević, Čebiševljeva i Markovljeva nejednakost u teoriji vjerojatnosti, Osječki matematički list 17 (2018), 125-137
   Abstract

   U ovom članku su, u vjerojatnosnom kontekstu, navedene i dokazane Čebiševljeva i Markovljeva nejednakost koje imaju značajnu primjenu u području teorije vjerojatnosti. Također, dani su primjeri problema iz svakodnevnoga života koji se mogu riješiti pomoću danih nejednakosti.
3. D. Jankov Maširević, M. Klarić, Primjena Bayesove formule i algoritamskog pristupa Bayesovoj formuli na situacijama iz svakodnevnog života, Math.e : hrvatski matematički elektronski časopis 31 (2017)
   Abstract

   U ovom članku je opisana Bayesova formula kao i algoritamski pristup korištenja Bayesove formule, koji je pogodan zbog jednostavnosti računanja uz upotrebu tablice (umjesto direktnog uvrštavanja u formulu). Također, dani su primjeri problema iz svakodnevnoga života čije je rješenje ilustrirano primjenom oba navedena pristupa.
4. D. Jankov Maširević, A. Kozić, Geometrijska vjerojatnost u svakodnevnom životu, Osječki matematički list (2015), prihvaćen za objavljivanje
5. D. Jankov Maširević, J. Jankov Pavlović, Zanimljive rekurzije, Matematičko fizički list 3/259 (2015)
6. D. Jankov Maširević, I. Papić, Tri klasična problema, Osječki matematički list 12 (2012), 11-19
7. D. Jankov Maširević, Egipatski razlomci, Osječki matematički list 11 (2011), 11-18

1. D. Jankov Maširević, Teorija odlučivanja, Sveučilište J. J. Strossmayera u Osijeku - Odjel za matematiku, Osijek, 2022.
2. D. Jankov Maširević, Zbirka riješenih zadataka iz teorije mjere i integracije, Sveučilište J.J.Strossmayera, Odjel za matematiku, Osijek, 2014.

Projects

• GAMe-based learning in MAthematics (GAMMA), Erasmus+ projekt  (KA201). Projekt was funded in 2020. and it ends in 2023. Project leader: izv. prof. dr. sc. Mirela Jukić Bokun
• Inequalities and Applications Project leader: prof. dr. sc. Josip Pečarić, University of Zagreb. Project was funded in 2014 by the Croatian Science Foundation.

• Problem procjene parametara u nekim dvoparametarskim monotonim matematičkim modelimaProject leader: doc. dr. sc. Darija Marković, Deptartment of Mathematics, University of Osijek. Project was funded by J. J. Strossmayer University of Osijek, since July 2013.
• Statistical Aspects of Parameter Estimation in Nonlinear Parametric ModelsProject leader: prof. dr. sc. Mirta Benšić, Deptartment of Mathematics, University of Osijek. Scientific project of the Croatian Ministry of Science, Education and Sports (235-2352818-1039).

Professional Activities

• upcoming conference:9th European Congress of Mathematics (9ECM 2024), 15-19 July 2024, Sevilla, Spain (short communication)
• upcoming conference: 8th Croatian Mathematical Congress, 2–5 July 2024, Osijek, Croatia (short communication)
• Harmonic analysis and distributions (HANDS 2024), April 10-12, 2024, Novi Sad, Serbia (short communication)
• The 6th International Conference “Mechanical Engineering in the 21st Century – MASING 2023”, 14-15 December 2023, Niš, Serbia (short communication)
• 7^th international conference on mathematics, “An Istanbul Meeting for World Mathematicians”, July 11-13, 2023, Istanbul, Turkey (short communication)
• Generalized Functions Online Workshop, May 12, 2023. (short communication)
• Harmonic analysis, spaces and operators (HASOP2023), April 19-21, 2023., Novi Sad, Serbia (short communication)
• The 8^th International Scientific Colloquium Mathematics and Children, May 28-29,  2021, Osijek, Croatia (short communication)
• 12th International Conference on Operational Research, September 24 – 26, 2008, Pula, Croatia (short communication)
• 2nd Conference of the Central European Network, September 12 – 16, 2011, Zurich, Switzerland (short communication)
• 16th Young Statisticians Meeting, October 14– 16, 2011, Rijeka, Croatia (short communication)
• 5th Croatian Mathematical Congress, June 18 – 21, 2012, Rijeka, Croatia (short communication)
• CINTI 2013, 14th IEEE International Symposium on Computational Intelligence and Informatics, November 19 – 21, 2013, Budapest, Hungary (short communication)
• 5th International Conference on Mathematics and Informatics, September 2 – 4, 2015, Targu Mures, Romania (short communication) 
• Workshop on Special Functions, September 8, 2015, Cluj-Napoca, Romania (short communication)
• 6th Croatian Mathematical Congress, June 14-17, 2016, Zagreb, Croatia (short communication)
• 15th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA), July, 22-26, 2019, Hagenberg, Austria (short communication)

• Since 2014. member of committee for teacher credentialing, appointed by Education and Teacher Training Agency.
• Zimska matematička škola (Winter math school):

• • 2018./2019. lecture – Primjena geometrijske vjerojatnosti u situacijama iz svakodnevnog života
  • 2012./2013. lecture – Zanimljive rekurzije
  • 2011./2012. lecture – Tri klasična problema
  • 2010./2011. lecture – Geometrijski medijan u ravnini
• Večer matematike
  • 2014./2015. lecture – Zanimljive rekurzije na djelu
  • 2019./2020. lecture -Kombinatorika i vjerojatnost – zajedno kroz ples 

Teaching

Winter semester (2023./2024.)

• Primijenjena matematika za računalnu znanost
• Realna analiza

Summer semester (2023./2024.)

• Teorija odlučivanja
• Linearna algebra II

Personal

• Birthdate: January 05, 1985
• Birthplace: Vukovar, Croatia
• Family: Married with Nikola, daughter Dunja, son Luka