The theory of orthogonal polynomials has matriarchal 

experienced an important development in recent 

decades. The first contact of our research group 

the question arose dearrollar to a method of Frobenius 

matriarchal matriarchal to solve differential equations 

second order without increasing the size of the problem. Of 

This appeared polynomial type solutions 

matriarchal matriarchal differential equations that 

widespread classical Hermite scalar equations, 

Laguerre; Legendre.En the PhD thesis of R. Company [3] and 

in the following [34], [35], [40], were introduced 

matriarchal Laguerre polynomials, Hermite and Gegenbauer, 

to verify certain properties of orthogonality 

nature not entirely transparent. 
We are then, having examples of classes 

specific orthogonal polynomials, the notion of unstructured 

orthogonality, although it had been published, including 

in an abstract, but next, results 

orthogonality of polynomials in a non-commutative algebra 

[10], [11]. 
The objective of this thesis is bidirectional: on the one hand it is 

well structured for the idea of orthogonality 

polynomials matriarchal, but with the intention to 

achieve the utility in applications that provide the 

families of classical orthogonal polynomials scalars. We 

thinking in the short term, in this work, using the idea of 

matriarchal ortoganalidad of polynomials to approximate 

matriarchal integrals, and also to develop fundiones 

in matriarchal matriarchal series of orthogonal polynomials. 
These ambitions have been influenced by the approach of 

Chiha [5] and the work of Stone [70] and Ghizzetti [29]. in 

memory solved some of the difficulties that appear 

and some answers are sumnistran, partially published 

in [36], [38], [39], [41], which are far from the final 

of the many goals in this line, we are 

can achieve. Among the questions to be solved subject to 

this work are: 
- Definition of orthogonality for polynomials 

matrilineal and matriarchal duties. 
- Structuring a regulated basis, where lie the 

orthogonal functions matriarchal. 
- Study the relationship of the rule base and the space 

concept of orthogonality in the absence of Hilbert space. 
- Solving the problem of best approximation matriarchal 

respect to a positive functional defined matriarchal. 
- Fourier Series matriarchal. 
- Collection of analogues of Riemann-Lebesgue Lemma and 

equality (inequality) Bessel-Parseval, in the absence of 

hilbertiana structure. 
- Introduction of the concept of totality for a family of 

orthogonal functions in the absence of matriarchal structure 

hilbertiana. 
- Possible development in series of orthogonal polynomials 

matrilineal (only for the case of Hermite) 
- Application development of the exponential of a matrix. 




The theory of orthogonal polynomials has matriarchal 

experienced an important development in recent 

decades. The first contact of our research group 

the question arose dearrollar to a method of Frobenius 

matriarchal matriarchal to solve differential equations 

second order without increasing the size of the problem. Of 

This appeared polynomial type solutions 

matriarchal matriarchal differential equations that 

widespread classical Hermite scalar equations, 

Laguerre; Legendre.En the PhD thesis of R. Company [3] and 

in the following [34], [35], [40], were introduced 

matriarchal Laguerre polynomials, Hermite and Gegenbauer, 

to verify certain properties of orthogonality 

nature not entirely transparent. 
We are then, having examples of classes 

specific orthogonal polynomials, the notion of unstructured 

orthogonality, although it had been published, including 

in an abstract, but next, results 

orthogonality of polynomials in a non-commutative algebra 

[10], [11]. 
The objective of this thesis is bidirectional: on the one hand it is 

well structured for the idea of orthogonality 

polynomials matriarchal, but with the intention to 

achieve the utility in applications that provide the 

families of classical orthogonal polynomials scalars. We 

thinking in the short term, in this work, using the idea of 

matriarchal ortoganalidad of polynomials to approximate 

matriarchal integrals, and also to develop fundiones 

in matriarchal matriarchal series of orthogonal polynomials. 
These ambitions have been influenced by the approach of 

Chiha [5] and the work of Stone [70] and Ghizzetti [29]. in 

memory solved some of the difficulties that appear 

and some answers are sumnistran, partially published 

in [36], [38], [39], [41], which are far from the final 

of the many goals in this line, we are 

can achieve. Among the questions to be solved subject to 

this work are: 
- Definition of orthogonality for polynomials 

matrilineal and matriarchal duties. 
- Structuring a regulated basis, where lie the 

orthogonal functions matriarchal. 
- Study the relationship of the rule base and the space 

concept of orthogonality in the absence of Hilbert space. 
- Solving the problem of best approximation matriarchal 

respect to a positive functional defined matriarchal. 
- Fourier Series matriarchal. 
- Collection of analogues of Riemann-Lebesgue Lemma and 

equality (inequality) Bessel-Parseval, in the absence of 

hilbertiana structure. 
- Introduction of the concept of totality for a family of 

orthogonal functions in the absence of matriarchal structure 

hilbertiana. 
- Possible development in series of orthogonal polynomials 

matrilineal (only for the case of Hermite) 
- Application development of the exponential of a matrix.