Extended Laguerre–Appell polynomials via fractional operators and their determinant forms
Extended Laguerre–Appell polynomials via fractional operators and their determinant forms
In this article, the extended form of Laguerre–Appell polynomials is introduced by means of generatingfunction and operational definition. The corresponding results for the extended Laguerre-Bernoulli and Laguerre-Eulerpolynomials are obtained as applications. Further, the determinant forms of these polynomials are established by usingoperational techniques.
___
- Andrews LC. Special Functions for Engineers and Applied Mathematicians. New York, NY, USA: Macmillan Publishing Company, 1985.
- Appell P. Sur une classe de polynômes. Ann Sci École Norm Sup 1880; 9: 119-144 (in French).
- Assante D, Cesarano C, Fornaro C, Vazquez L. Higher order and fractional diffusive equations. Journal of Engineering Science and Technology Review 2015; 8: 202-204.
- Costabile FA. On expansion of a real function in Bernoulli polynomials and applications. Conferenze del sem Matem Uni Bari (IT) n 273 1999.
- Costabile FA, Dell′ Accio F, Gualtieri MI. A new approach to Bernoulli polynomials. Rend Mat Appl 2006; 26: 1-12.
- Costabile FA, Longo E. A determinantal approach to Appell polynomials. J Comput Appl Math 2010; 234: 1528- 1542.
- Costabile FA, Longo E. An algebraic approach to Sheffer polynomial sequences. Integral Transforms Spec Funct 2014; 25: 295-311.
- Costabile FA, Longo E. An algebraic exposition of umbral calculus with application to general interpolation problem - a survey. Publications de L′ institut Mathématique Nouvelle série, tome 2014; 96: 67-83.
- Dattotli G, Lorenzutta S, Cesarano C. Bernstein polynomials and operational methods. J Comput Anal Appl 2006; 8: 369-377.
- Dattoli G, Ricci PE, Cesarano C, Vázquez L. Special polynomials and fractional calculus. Math Comput Modelling 2003; 37: 729-733.
- Dattoli G, Torre A. Operational methods and two variable Laguerre polynomials. Atti Acad Sci Torino CL Sci Fis Mat Natur 1998; 132: 1-7.
- Khan S, Al-Saad MWM, Khan R. Laguerre-based Appell polynomials: properties and applications. Math Comput Modelling 2010; 52: 247-259.
- Khan S, Yasmin G, Khan R, Hassan NAM. Hermite-based Appell polynomials: properties and applications. J Math Anal Appl 2009; 351;: 756-764.
- Magnus W, Oberhettinger F, Soni RP. Formulas and Theorems for Special Functions of Mathematical Physics. New York, NY, USA: Springer-Verlag, 1956.
- Oldham H, Spanier N. The Fractional Calculus. San Diego, CA, USA: Academic Press, 1974.
- Widder DV. An Introduction to Transform Theory. New York, NY, USA: Academic Press, 1971.
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
Sayıdaki Diğer Makaleler
Somphong JITMAN, Rattana SRITHUS, Chalermpong WORAWANNOTAI
On the rank of transformation semigroup T(n,m)
Combinatorial enumeration of cyclic covers of $\mathbb{P}^{1}$
Alberto BESANA, Cristina Martinez RAMIREZ
Block classical Gram–Schmidt-based block updating in low-rank matrix approximation
Hasan ERBAY, Cenker BİÇER, Fahrettin HORASAN, Fatih VARÇIN
Prasanta Kumar RAY, Nurettin IRMAK, Bijan Kumar PATEL
Hari SRIVASTAVA, Rabha ELASHWAH, W KOTA