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2015 | 13 | 1 |
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The Umbral operator and the integration involving generalized Bessel-type functions

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The main purpose of this paper is to introduce a class of new integrals involving generalized Bessel functions and generalized Struve functions by using operational method and umbral formalization of Ramanujan master theorem. Their connections with trigonometric functions with several distinct complex arguments are also presented.
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  • Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University,
    Wadi Aldawaser, Riyadh region, 11991, Saudi Arabia
  • Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa, 31982,
    Saudi Arabia
  • Department of Mathematics, Anand International College of Engineering, Jaipur-303012,
    Republic of India
  • Department of Systems Engineering, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
  • [1] T. Amdeberhan and V. H. Moll, A formula for a quartic integral: a survey of old proofs and some new ones, Ramanujan J. 18 (2009), no. 1, 91–102. [Crossref][WoS]
  • [2] T. Amdeberhan,O. Espinosa, I. Gonzalez, M. Harrison, V. H. Moll and A. Straub, Ramanujan’s master theorem, Ramanujan J. 29 (2012), no. 1-3, 103–120. [Crossref][WoS]
  • [3] P. E. Appell and J. Kampé de Férit, Fonctions Hypergeometriques et Polynomes d’Hermite, Gauthier-Villars, Paris, 1926.
  • [4] D. Babusci, G. Dattoli, G. H. E. Duchamp, Góska and K. A. Penson, Definite integrals and operational methods, Appl. Math. Comput. 219 (2012), no. 6, 3017–3021. [WoS]
  • [5] D. Babusci and G. Dattoli, On Ramanujan Master Theorem, arXiv:1103.3947 [WoS]
  • [math-ph].
  • [6] D. Babusci, G. Dattoli, B. Germano, M. R. Martinelli and P.E. Ricci, Integrals of Bessel functions, Appl. Math. Lett. 26 (2013), no. 3, 351–354. [Crossref]
  • [7] B. C. Berndt, Ramanujan’s notebooks. Part I, Springer, New York, 1985.
  • [8] Á. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen 73 (2008), no. 1-2, 155–178.
  • [9] K. Górska, D. Babusci, G. Dattoli, G. H. E. Duchamp and K. A. Penson, The Ramanujan master theorem and its implications for special functions, Appl. Math. Comput. 218 (2012), no. 23, 11466–11471. [WoS]
  • [10] I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, fifth edition, Academic Press, San Diego, CA, 1996.
  • [11] G. H. Hardy, Ramanujan. Twelve lectures on subjects suggested by his life and work, Cambridge Univ. Press, Cambridge, England, 1940.
  • [12] S. R. Mondal and A. Swaminathan, Geometric properties of generalized Bessel functions, Bull. Malays. Math. Sci. Soc. (2) 35 (2012), no. 1, 179–194.
  • [13] R. Mullin and G.-C. Rota. On the foundations of combinatorial theory III. Theory of binomial enumeration. In B. Harris, editor, Graph theory and its applications, Academic Press, 1970, 167–213.
  • [14] G.-C. Rota. The number of partitions of a set. Amer. Math. Monthly, (1964),no. 71, 498–504. [Crossref]
  • [15] G.-C. Rota. Finite operator calculus. Academic Press, New York, 1975.
  • [16] G.-C. Rota and B.D. Taylor. An introduction to the umbral calculus. In H.M. Srivastava and Th.M. Rassias, editors, Analysis, Geometry and Groups: A Riemann Legacy Volume, Palm Harbor, Hadronic Press, 1993, 513–525.
  • [17] G.-C. Rota and B.D. Taylor. The classical umbral calculus. SIAM J. Math. Anal.,(1994),no 25, 694–711.
  • [18] S. Roman, The Umbral Calculus (Academic Press, INC, Orlando, 1984).
  • [19] H. M. Srivastava and H. L. Manocha, A treatise on generating functions, Ellis Horwood Series: Mathematics and its Applications, Horwood, Chichester, 1984.
  • [20] F. G. Tricomi, Funzioni ipergeometriche confluenti (Italian), Ed. Cremonese, Roma, 1954.
  • [21] N. Yagmur and H. Orhan, Starlikeness and convexity of generalized Struve functions, Abstr. Appl. Anal. 2013, Art. ID 954513, 6 pp. [WoS]
  • [22] H. W. Gould and A. T. Hopper, Operational formulas connected with two generalizations of Hermite polynomials, Duke Math. J. 29 (1962), 51–63. [Crossref]
  • [23] G. Maroscia and P. E. Ricci, Hermite-Kampé de Fériet polynomials and solutions of boundary value problems in the half-space, J. Concr. Appl. Math. 3 (2005), no. 1, 9–29.
  • [24] G. Dattoli et al., Evolution operator equations: integration with algebraic and finite-difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory, Riv. Nuovo Cimento Soc. Ital. Fis. (4) 20 (1997), no. 2, 3–133.
  • [25] G. Dattoli, P. E. Ricci and C. Cesarano, Monumbral polynomials and the associated formalism, Integral Transforms Spec. Funct. 13 (2002), no. 2, 155–162.
  • [26] G. Dattoli, P. E. Ricci and C. Cesarano, Beyond the monomiality: the monumbrality principle, J. Comput. Anal. Appl. 6 (2004), no. 1, 77–83.
  • [27] C. Cesarano, D. Assante, A note on Generalized Bessel Functions, International Journal of Mathematical Models and Methods in Applied Sciences, vol. 7, p. 625–629
  • [28] G. Dattoli, C. Cesarano and D. Sacchetti, A note on truncated polynomials, Appl. Math. Comput. 134 (2003), no. 2-3, 595–605. [Crossref]
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