Solutions of Tridiagonal Recurrence Relations, Application to Ordinary and Partial Differential Equations

1984 ◽  
pp. 196-228 ◽  
Author(s):  
Hannes Risken
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Recurrence Relations ◽  
Partial Differential

Some new results for the multivariable Humbert polynomials

2014 ◽  
Vol 64 (6) ◽  
Author(s):  
Rabıa Aktaş
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Representation ◽  
Recurrence Relations ◽  
Addition Formula ◽  
Partial Differential ◽  
Special Cases ◽  
Humbert Polynomials

AbstractIn this paper, we present some miscellaneous properties of the multivariable Humbert polynomials whose special cases include some well-known multivariable polynomials such as Chan-Chyan-Srivastava, Lagrange-Hermite and Erkus-Srivastava multivariable polynomials. We give recurrence relations, addition formula and integral representation for them. Then, we obtain some partial differential equations for the products of the multivariable Humbert polynomials and some other multivariable polynomials. Furthermore, some special cases of the results presented in this study are also indicated.

scholarly journals Müntz sturm-liouville problems: Theory and numerical experiments

2021 ◽  
Vol 24 (3) ◽  
pp. 775-817
Author(s):  
Hassan Khosravian-Arab ◽  
Mohammad Reza Eslahchi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Bounds ◽  
Spectral Properties ◽  
Numerical Experiments ◽  
Recurrence Relations ◽  
Basis Functions ◽  
Partial Differential ◽  
Orthogonal Projections ◽  
Sturm Liouville

Abstract This paper presents two new classes of Müntz functions which are called Jacobi-Müntz functions of the first and second types. These newly generated functions satisfy in two self-adjoint fractional Sturm-Liouville problems and thus they have some spectral properties such as: orthogonality, completeness, three-term recurrence relations and so on. With respect to these functions two new orthogonal projections and their error bounds are derived. Also, two new Müntz type quadrature rules are introduced. As two applications of these basis functions some fractional ordinary and partial differential equations are considered and numerical results are given.

On some classes of differential equations and associated integral equations for the Laguerre–Appell polynomials

2018 ◽  
Vol 9 (3) ◽  
pp. 185-194 ◽  
Author(s):  
Subuhi Khan ◽  
Mumtaz Riyasat ◽  
Shahid Ahmad Wani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Equations ◽  
Recurrence Relations ◽  
Laguerre Polynomials ◽  
Factorization Method ◽  
Volterra Integral Equations ◽  
Appell Polynomials ◽  
Partial Differential ◽  
Genocchi Polynomials

Abstract The article aims to explore some new classes of differential equations and associated integral equations for some hybrid families of Laguerre polynomials. The recurrence relations and differential, integro-differential and partial differential equations for the hybrid Laguerre–Appell polynomials are derived via the factorization method. An analogous study of these results for the hybrid Laguerre–Bernoulli, Euler and Genocchi polynomials is presented. Further, the Volterra integral equations for the hybrid Laguerre–Appell polynomials and for their corresponding members are also explored.

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