Some Results of Fractional Integral Involving I-Function and General Class of Polynomial

Abstract

In the present paper, we have derived two multiplication theorems for I-function by using fractional integral formula \( \mathop I\nolimits_{0,x}^{\alpha ,\beta ,\eta } f(x) \) and \( \mathop J\nolimits_{0,\infty }^{\alpha ,\beta ,\eta } f(x) \) (Banerji and Choudhary in Proc Natl Acad Sci India Sect A Phys Sci 66:271–278, 1996). Further, we established some applications of the theorem in the form of particular case.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Banerji, P.K., Choudhary, S.: Fractional integral formulae involving general class of polynomials. Proc Natl Acad Sci India Sect A Phys Sci 66, 271–278 (1996)

    MathSciNet  MATH  Google Scholar 

  2. 2.

    Saxena, V.P.: Formal solutions of certain new pair of dual integral equation involving H-function. Proc Natl Acad Sci India Sect A Phys Sci 52A, 366–375 (1982)

    MathSciNet  MATH  Google Scholar 

  3. 3.

    Sharma, C.K., Shrivastava, H.M.: Some expansion formulae for the I-function. Proc Natl Acad Sci India Sect A Phys Sci 62A, 236–239 (1992)

    MathSciNet  MATH  Google Scholar 

  4. 4.

    Seigo, M.: A certain boundary value problem for the Darboux equation. Math Jpn 24, 377–385 (1979)

    MathSciNet  Google Scholar 

  5. 5.

    Srivastava, H.M.: A contour integral involving Fox’s H-function. Indian J Math 14, 1–6 (1972)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are thankful to the editor-in-chief Professor Santanu Saha Ray and learned reviewer for their valuable comments towards the improvements of the manuscript.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Bhupendra Tripathi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tripathi, B., Sharma, R. & Sharma, C.K. Some Results of Fractional Integral Involving I-Function and General Class of Polynomial. Int. J. Appl. Comput. Math 6, 103 (2020). https://doi.org/10.1007/s40819-020-00855-w

Download citation

Keywords

  • Analytic functions
  • Univalent functions
  • Inverse functions

Mathematics Subject Classification

  • 30C45
  • 11B65