Research Article
Year 2025,
Volume: 54 Issue: 3, 921 - 927, 24.06.2025
Abstract
The Leibniz integral rule enables us to interchange the order of differentiation and integration under some differentiability conditions on the functions. It can be very useful in the computing the exact value of certain integrals. In this paper, we will present analogs of such rule for $q$-integrals with functional borders and their properties.
Keywords
Supporting Institution
Ministry of Education, Science and Technological Development of the Republic of Serbia.
References
- [1] G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge, England, Cambridge University Press, 2004.
- [2] R.P. Feynman, A Different Set of Tools, In ’Surely You’re Joking, Mr. Feynman!’: Adventures of a Curious Character, New York, W. W. Norton, 1997.
- [3] G. Gasper and M. Rahman, Basic Hypergeometric Series, 2nd ed. Encyclopedia of Mathematics and its Applications 96, Cambridge University Press, 2004.
- [4] W. Hahn, Lineare Geometrische Differenzengleichungen, Berichte der Mathematisch- Statistischen Section im Forschungszentrum Graz, 1981.
- [5] I.T. Huseynov, A. Ahmadova and N.I. Mahmudov, Fractional Leibniz integral rules for Riemann–Liouville and Caputo fractional derivatives and their applications, arXiv:2012.11360v1 [math.CA].
- [6] V. Kac and P. Cheung, Quantum Calculus, Springer–Verlag, New York, 2002.
- [7] W. Koepf, Hypergeometric Summation, Advanced Lectures in Mathematics, Vieweg, Braunschweig/Wiesbaden, 1998.
- [8] P.M. Rajkovic, M.S. Stankovic and S.D. Marinkovic, Mean value theorems in q–calculus, Matematicki vesnik 54, 171–178, 2002.
- [9] F.S. Woods, Differentiation of a Definite Integral, Advanced Calculus: A Course Arranged with Special Reference to the Needs of Students of Applied Mathematics, 141–144, Boston, Ginn, 1926.
Year 2025,
Volume: 54 Issue: 3, 921 - 927, 24.06.2025
Abstract
References
- [1] G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge, England, Cambridge University Press, 2004.
- [2] R.P. Feynman, A Different Set of Tools, In ’Surely You’re Joking, Mr. Feynman!’: Adventures of a Curious Character, New York, W. W. Norton, 1997.
- [3] G. Gasper and M. Rahman, Basic Hypergeometric Series, 2nd ed. Encyclopedia of Mathematics and its Applications 96, Cambridge University Press, 2004.
- [4] W. Hahn, Lineare Geometrische Differenzengleichungen, Berichte der Mathematisch- Statistischen Section im Forschungszentrum Graz, 1981.
- [5] I.T. Huseynov, A. Ahmadova and N.I. Mahmudov, Fractional Leibniz integral rules for Riemann–Liouville and Caputo fractional derivatives and their applications, arXiv:2012.11360v1 [math.CA].
- [6] V. Kac and P. Cheung, Quantum Calculus, Springer–Verlag, New York, 2002.
- [7] W. Koepf, Hypergeometric Summation, Advanced Lectures in Mathematics, Vieweg, Braunschweig/Wiesbaden, 1998.
- [8] P.M. Rajkovic, M.S. Stankovic and S.D. Marinkovic, Mean value theorems in q–calculus, Matematicki vesnik 54, 171–178, 2002.
- [9] F.S. Woods, Differentiation of a Definite Integral, Advanced Calculus: A Course Arranged with Special Reference to the Needs of Students of Applied Mathematics, 141–144, Boston, Ginn, 1926.
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Real and Complex Functions (Incl. Several Variables), Mathematical Methods and Special Functions |
| Journal Section | Mathematics |
| Authors | |
| Early Pub Date | January 27, 2025 |
| Publication Date | June 24, 2025 |
| Submission Date | December 18, 2023 |
| Acceptance Date | August 19, 2024 |
| Published in Issue | Year 2025 Volume: 54 Issue: 3 |