The generalized Struve function

1Virchenko, NO, 1Ovcharenko, OV
1NTU of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
Dopov. Nac. akad. nauk Ukr. 2018, 5:3-7
https://doi.org/10.15407/dopovidi2018.05.003
Section: Mathematics
Language: Ukrainian
Abstract: 
The new generalization of the Struve function is introduced, its connection with the confluent hypergeometric function $_{1}F_{2}$ and with the Bessel function $I_{v+1}(z)$ is given. The examples of applications of the generalized Struve function are given.
Keywords: confluent hypergeometric function, Struve function
References: 
  1. Andrews, G., Askey, R. & Roy, R. (1999). Special Functions. New York: Cambridge Univ. Press. doi: https://doi.org/10.1017/CBO9781107325937
  2. Virchenko, N. O. & Tsarenko, V. N. (1995). Fractional integral transforms of hypergeometric type. Kiev.
  3. Virchenko, N. O. (2016). Generalized hypergeometric functions. Kiev: NTUU "KPI".
  4. Aomoto, K. (1996). Hypergeometric functions: the past, today and … (from the complex analytic point of view). Sugaku Expositions, 9, pp. 99-116.
  5. Barnard, R. W. (1999). On application of hypergeometric functions. J. Comput. Appl. Math., 105, No. 1-2, pp. 1-8. doi: https://doi.org/10.1016/S0377-0427(99)00010-2
  6. Barnes, E. W. (1908). A new development of certain hypergeometric functions. Proc. London Math. Soc., 6, pp.141-177. doi: https://doi.org/10.1112/plms/s2-6.1.141
  7. Chaudhry M.A., Qadir A., Srivastava H.M. & Paris R.B. (2004). Extended hypergeometric and confluent hypergeometric function. Appl. Math. Comput., 159, pp. 589-602. doi: https://doi.org/10.1016/j.amc.2003.09.017
  8. Galue, L. (2008). Results involving generalized hypergeometric functions. Math. Balkanica, New Ser., 22, No. 1-2, pp. 83-100.
  9. Joshi, C. M., Vyas, Y. (2003). Extensions of certain classical integral of Erdelyi for Gauss hypergeometric functions. J. Comput. Appl. Math., 160, pp. 125-138. doi: https://doi.org/10.1016/S0377-0427(03)00619-8
  10. Qadir, A. (2007). The generalization of special functions. Appl. Math. Comput., 187, pp. 395-402. doi: https://doi.org/10.1016/j.amc.2006.08.138
  11. Virchenko, N. O. (1999). On some generalizations of the functions of hypergeometric type. Fract. Calc. Appl. Anal., 2, No. 3, pp. 233-244.
  12. Virchenko, N. O., Kalla, S. L. & Al-Zamel, A. (2001). Some results on a generalized hypergeometric function. Integr. Transf. Spec. Funct., 12, No. 1, pp. 89-100. doi: https://doi.org/10.1080/10652460108819336
  13. Virchenko, N. O. (2013). On the r-generalized confluent hypergeometric function. J. Inequal. Spec. Funct., 4, No. 1, pp. 47-52.
  14. Wright, E. M. (1935). The asymptotic expansion of the generalized hypergeometric function. J. London Math. Soc., 10, pp. 286-293. doi: https://doi.org/10.1112/jlms/s1-10.40.286
  15. Bateman, H. (1974). Higher transcendental functions. Vol. 2. Bessel functions, functions of parabolic cylinder, orthogonal polynomials. Moscow: Nauka.