In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermit...In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermite matrix polynomials,the orthogonality property and a Rodrigues' formula are given.展开更多
In this paper we are looking forward to finding the approximate analytical solutions for fractional integro-differential equations by using Sumudu transform method and Hermite spectral collocation method.The fractiona...In this paper we are looking forward to finding the approximate analytical solutions for fractional integro-differential equations by using Sumudu transform method and Hermite spectral collocation method.The fractional derivatives are described in the Caputo sense.The applications related to Sumudu transform method and Hermite spectral collocation method have been developed for differential equations to the extent of access to approximate analytical solutions of fractional integro-differential equations.展开更多
In this paper,we introduce mon-symbolic method to obtain the generating functions of the hybrid class of Hermite-associated Laguerre and its associated polynomials.We obtain the series definitions of these hybrid spec...In this paper,we introduce mon-symbolic method to obtain the generating functions of the hybrid class of Hermite-associated Laguerre and its associated polynomials.We obtain the series definitions of these hybrid special polynomials.Also,we derive the double lacunary generating functions of the Hermite-Laguerre polynomials and the Hermite-Laguerre-Wright polynomials.Further,we find multiplicative and derivative operators for the Hermite-Laguerre-Wright polynomials which helps to find the symbolic differential equation of the Hermite-Laguerre-Wright polynomials.Some concluding remarks are also given.展开更多
In this work we develop necessary and sufficient conditions for describing the family of anti-Hurwitz polynomials, introduced by Vergara-Hermosilla <em>et al</em>. in [1]. Specifically, we studied a dual v...In this work we develop necessary and sufficient conditions for describing the family of anti-Hurwitz polynomials, introduced by Vergara-Hermosilla <em>et al</em>. in [1]. Specifically, we studied a dual version of the Theorem of Routh-Hurwitz and present explicit criteria for polynomials of low order and derivatives. Another contribution of this work is establishing a dual version of the Hermite-Biehler Theorem. To this aim, we give extensions of the boundary crossing Theorems and a zero exclusion principle for anti-Hurwitz polynomials.展开更多
The tangent polynomials Tn(z)are generalization of tangent numbers or the Euler zigzag numbers Tn.In particular,Tn(0)=Tn.These polynomials are closely related to Bernoulli,Euler and Genocchi polynomials.One of the ext...The tangent polynomials Tn(z)are generalization of tangent numbers or the Euler zigzag numbers Tn.In particular,Tn(0)=Tn.These polynomials are closely related to Bernoulli,Euler and Genocchi polynomials.One of the extensions and analogues of special polynomials that attract the attention of several mathematicians is the Apostol-type polynomials.One of these Apostol-type polynomials is the Apostol-tangent polynomials Tn(z,λ).Whenλ=1,Tn(z,1)=Tn(z).The use of hyperbolic functions to derive asymptotic approximations of polynomials together with saddle point method was applied to the Bernoulli and Euler polynomials by Lopez and Temme.The same method was applied to the Genocchi polynomials by Corcino et al.The essential steps in applying the method are(1)to obtain the integral representation of the polynomials under study using their exponential generating functions and the Cauchy integral formula,and(2)to apply the saddle point method.It is found out that the method is applicable to Apostol-tangent polynomials.As a result,asymptotic approximation of Apostol-tangent polynomials in terms of hyperbolic functions are derived for large values of the parameter n and uniform approximation with enlarged region of validity are also obtained.Moreover,higher-order Apostol-tangent polynomials are introduced.Using the same method,asymptotic approximation of higherorder Apostol-tangent polynomials in terms of hyperbolic functions are derived and uniform approximation with enlarged region of validity are also obtained.It is important to note that the consideration of Apostol-type polynomials and higher order Apostol-type polynomials were not done by Lopez and Temme.This part is first done in this paper.The accuracy of the approximations are illustrated by plotting the graphs of the exact values of the Apostol-tangent and higher-order Apostol-tangent polynomials and their corresponding approximate values for specific values of the parameters n,λand m.展开更多
文摘In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermite matrix polynomials,the orthogonality property and a Rodrigues' formula are given.
文摘In this paper we are looking forward to finding the approximate analytical solutions for fractional integro-differential equations by using Sumudu transform method and Hermite spectral collocation method.The fractional derivatives are described in the Caputo sense.The applications related to Sumudu transform method and Hermite spectral collocation method have been developed for differential equations to the extent of access to approximate analytical solutions of fractional integro-differential equations.
文摘In this paper,we introduce mon-symbolic method to obtain the generating functions of the hybrid class of Hermite-associated Laguerre and its associated polynomials.We obtain the series definitions of these hybrid special polynomials.Also,we derive the double lacunary generating functions of the Hermite-Laguerre polynomials and the Hermite-Laguerre-Wright polynomials.Further,we find multiplicative and derivative operators for the Hermite-Laguerre-Wright polynomials which helps to find the symbolic differential equation of the Hermite-Laguerre-Wright polynomials.Some concluding remarks are also given.
文摘In this work we develop necessary and sufficient conditions for describing the family of anti-Hurwitz polynomials, introduced by Vergara-Hermosilla <em>et al</em>. in [1]. Specifically, we studied a dual version of the Theorem of Routh-Hurwitz and present explicit criteria for polynomials of low order and derivatives. Another contribution of this work is establishing a dual version of the Hermite-Biehler Theorem. To this aim, we give extensions of the boundary crossing Theorems and a zero exclusion principle for anti-Hurwitz polynomials.
基金funded by Cebu Normal University through its Research Institute for Computational Mathematics and Physics(RICMP).
文摘The tangent polynomials Tn(z)are generalization of tangent numbers or the Euler zigzag numbers Tn.In particular,Tn(0)=Tn.These polynomials are closely related to Bernoulli,Euler and Genocchi polynomials.One of the extensions and analogues of special polynomials that attract the attention of several mathematicians is the Apostol-type polynomials.One of these Apostol-type polynomials is the Apostol-tangent polynomials Tn(z,λ).Whenλ=1,Tn(z,1)=Tn(z).The use of hyperbolic functions to derive asymptotic approximations of polynomials together with saddle point method was applied to the Bernoulli and Euler polynomials by Lopez and Temme.The same method was applied to the Genocchi polynomials by Corcino et al.The essential steps in applying the method are(1)to obtain the integral representation of the polynomials under study using their exponential generating functions and the Cauchy integral formula,and(2)to apply the saddle point method.It is found out that the method is applicable to Apostol-tangent polynomials.As a result,asymptotic approximation of Apostol-tangent polynomials in terms of hyperbolic functions are derived for large values of the parameter n and uniform approximation with enlarged region of validity are also obtained.Moreover,higher-order Apostol-tangent polynomials are introduced.Using the same method,asymptotic approximation of higherorder Apostol-tangent polynomials in terms of hyperbolic functions are derived and uniform approximation with enlarged region of validity are also obtained.It is important to note that the consideration of Apostol-type polynomials and higher order Apostol-type polynomials were not done by Lopez and Temme.This part is first done in this paper.The accuracy of the approximations are illustrated by plotting the graphs of the exact values of the Apostol-tangent and higher-order Apostol-tangent polynomials and their corresponding approximate values for specific values of the parameters n,λand m.
