2-Variable Fubini-degenerate Apostol-type polynomials

2021 ◽  
pp. 2250092
Author(s):  
Tabinda Nahid ◽  
Cheon Seoung Ryoo
Keyword(s):  
Series Expansion ◽  
Difference Equations ◽  
Graphical Representations ◽  
Interesting Pattern ◽  
Explicit Representations ◽  
Connection Formulas

This work deals with the mathematical inspection of a hybrid family of the degenerate polynomials of the Apostol-type. The inclusion of the derivation of few series expansion formulas, explicit representations and difference equations for this hybrid family brings a novelty to the existing literature. Moreover, certain connection formulas and several novel identities for these polynomials are established and investigated. The graphical representations of certain degenerate polynomials are explored and several new interesting pattern of the zeros are observed.

scholarly journals Computational Analysis of Generalized Zeta Functions by Using Difference Equations

2020 ◽  
Author(s):  
Asifa Tassaddiq
Keyword(s):  
Difference Equations ◽  
Taylor Series ◽  
Computational Analysis ◽  
Zeta Functions ◽  
Series Expansions ◽  
Graphical Representations ◽  
Computational Power ◽  
Numerical Computations ◽  
Taylor Series Expansions

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

scholarly journals On Second Order q-Difference Equations Satisfied by Al-Salam–Carlitz I-Sobolev Type Polynomials of Higher Order

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1300
Author(s):  
Carlos Hermoso ◽  
Edmundo J. Huertas ◽  
Alberto Lastra ◽  
Anier Soria-Lorente
Keyword(s):  
Orthogonal Polynomials ◽  
Real Number ◽  
Difference Equations ◽  
Arbitrary Number ◽  
Recurrence Formula ◽  
Second Order ◽  
Inner Product ◽  
Sobolev Type ◽  
Ladder Operators ◽  
Connection Formulas

This contribution deals with the sequence {Un(a)(x;q,j)}n≥0 of monic polynomials in x, orthogonal with respect to a Sobolev-type inner product related to the Al-Salam–Carlitz I orthogonal polynomials, and involving an arbitrary number j of q-derivatives on the two boundaries of the corresponding orthogonality interval, for some fixed real number q∈(0,1). We provide several versions of the corresponding connection formulas, ladder operators, and several versions of the second order q-difference equations satisfied by polynomials in this sequence. As a novel contribution to the literature, we provide certain three term recurrence formula with rational coefficients satisfied by Un(a)(x;q,j), which paves the way to establish an appealing generalization of the so-called J-fractions to the framework of Sobolev-type orthogonality.

Towards the Affective Cognition Approach to Human Performance in Space

2020 ◽  
Vol 91 (6) ◽  
pp. 532-534
Author(s):  
Nicola Mammarella
Keyword(s):  
Cognitive Performance ◽  
Cognitive Processing ◽  
Human Performance ◽  
Space Missions ◽  
Cognition And Emotion ◽  
Dynamic Relation ◽  
Interesting Pattern

INTRODUCTION: In recent decades, there has been investigation into the effects of microgravity and microgravity-like environments on cognition and emotion separately. Here we highlight the need of focusing on emotion-cognition interactions as a framework for explaining cognitive performance in space. In particular, by referring to the affective cognition hypothesis, the significant interplay between emotional variables and cognitive processing in space is briefly analyzed. Altogether, this approach shows an interesting pattern of data pointing to a dynamic relation that may be sensitive to microgravity. The importance of examining interactions between emotion and cognition for space performance remains fundamental (e.g., stress-related disorders) and deserves further attention. This approach is ultimately interesting considering the potential effects that microgravity may play on human performance during long-term space missions and on return to Earth.Mammarella N. Towards the affective cognition approach to human performance in space. Aerosp Med Hum Perform. 2020; 91(6):532–534.

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