Araştırma Makalesi
Yıl 2025,
, 921 - 927, 24.06.2025
Öz
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.
Anahtar Kelimeler
Destekleyen Kurum
Ministry of Education, Science and Technological Development of the Republic of Serbia.
Kaynakça
- [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.
Yıl 2025,
, 921 - 927, 24.06.2025
Öz
Kaynakça
- [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.
Toplam 9 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Reel ve Kompleks Fonksiyonlar, Matematiksel Yöntemler ve Özel Fonksiyonlar |
| Bölüm | Matematik |
| Yazarlar | |
| Erken Görünüm Tarihi | 27 Ocak 2025 |
| Yayımlanma Tarihi | 24 Haziran 2025 |
| Gönderilme Tarihi | 18 Aralık 2023 |
| Kabul Tarihi | 19 Ağustos 2024 |
| Yayımlandığı Sayı | Yıl 2025 |