Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A STUDY OF NEW CLASS OF INTEGRALS ASSOCIATED WITH GENERALIZED STRUVE FUNCTION AND POLYNOMIALS

  • Haq, Sirazul (Department of Applied Mathematics Faculty of Engineering and Technology Aligarh Muslim University) ;
  • Khan, Abdul Hakim (Department of Applied Mathematics Faculty of Engineering and Technology Aligarh Muslim University) ;
  • Nisar, Kottakkaran Sooppy (Department of Mathematics College of Arts and Science Prince Sattam bin Abdulaziz University)
  • Received : 2017.12.23
  • Accepted : 2018.03.01
  • Published : 2019.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

The main aim of this paper is to establish a new class of integrals involving the generalized Galu$Galu{\grave{e}}$-type Struve function with the different type of polynomials such as Jacobi, Legendre, and Hermite. Also, we derive the integral formula involving Legendre, Wright generalized Bessel and generalized Hypergeometric functions. The results obtained here are general in nature and can deduce many known and new integral formulas involving the various type of polynomials.

Keywords

References

  1. A. Baricz, Generalized Bessel Functions of the First Kind, Lecture Notes in Mathematics, 1994, Springer-Verlag, Berlin, 2010.
  2. K. N. Bhowmick, Some relations between a generalized Struve's function and hypergeometric functions, Vijnana Parishad Anusandhan Patrika 5 (1962), 93-99.
  3. K. N. Bhowmick, A generalized Struve's function and its recurrence formula, Vijnana Parishad Anusandhan Patrika 6 (1963), 1-11.
  4. A. Erdelyi and H. Bateman, Higher Transcendental Functions. Vol. 1, McGraw Hill, 1953.
  5. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. Vol. 3, McGraw-Hill, New York, NY USA, 1955.
  6. L. Galue, A generalized Bessel function, Integral Transforms Spec. Funct. 14 (2003), no. 5, 395-401. https://doi.org/10.1080/1065246031000074362
  7. B. N. Kanth, Integrals involving generalised Struve's function, Nepali Math. Sci. Rep. 6 (1981), no. 1-2, 61-64.
  8. V. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Research Notes in Mathematics Series, 301, Longman Scientific & Technical, Harlow, 1994.
  9. K. S. Nisar, D. Baleanu, and M. M. Al-Qurashi, Fractional calculus and application of generalized Struve function, SpringerPlus, 2016 (2016), DOI 10.1186/s40064-016-2560-3.
  10. H. Orhan and N. Yagmur, Geometric properties of generalized Struve functions, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 63 (2017), no. 2, 229-244.
  11. E. D. Rainville, Special Functions, reprint of 1960 first edition, Chelsea Publishing Co., Bronx, NY, 1971.
  12. V. P. Saxena, The I-Function, Anamaya publisher, New Delhi, 2008.
  13. R. P. Singh, Generalized Struve's function and its recurrence relations, Ranchi Univ. Math. J. 5 (1974), 67-75.
  14. R. P. Singh, Generalized Struve's function and its recurrence equation, Vijnana Parishad Anusandhan Patrika 28 (1985), no. 3, 287-292
  15. R. P. Singh, Some integral representation of generalized Struve's function, Math. Ed. (Siwan) 22 (1988), no. 3, 91-94.
  16. R. P. Singh, Infinite integrals involving generalized Struve function, Math. Ed. (Siwan) 23 (1989), no. 1, 30-36.
  17. H. M. Srivastava and J. Choi, Zeta and q-Zeta functions and associated series and integrals, Elsevier, Inc., Amsterdam, 2012.
  18. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester, 1985.
  19. H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester, 1984.
  20. E. M. Wright, The asymptotic expansion of the generalized Bessel function, Proc. London Math. Soc. (2) 38 (1935), 257-270. https://doi.org/10.1112/plms/s2-38.1.257
  21. E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, J. London Math. Soc. 10 (1935), 286-293. https://doi.org/10.1112/jlms/s1-10.40.286
  22. N. Yagmur and H. Orhan, Starlikeness and convexity of generalized Struve functions, Abstr. Appl. Anal. 2013 (2013), Art. ID 954513, 6 pp.