scholarly journals On generalized Lagrange–Hermite–Bernoulli and related polynomials

2020 ◽  
Vol 23 (2) ◽  
pp. 211-224
Author(s):  
Waseem A. Khan ◽  
M. A. Pathan
Keyword(s):  
Generating Functions ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Point Of View ◽  
Generalized Polynomials ◽  
New Class ◽  
The Past ◽  
The Family ◽  
Generating Relations ◽  
High Degree

We introduce a new class of generalized polynomials, ascribed to the family of Hermite, Lagrange, Bernoulli, Miller–Lee, and Laguerre polynomials and of their associated forms. These polynomials can be expressed in the form of generating functions, which allow a high degree of exibility for the formulation of the relevant theory. We develop a point of view based on generating relations, exploited in the past, to study some aspects of the theory of special functions. We propose a fairly general analysis allowing a transparent link between different forms of special polynomials.

scholarly journals An Extension of Caputo Fractional Derivative Operator by Use of Wiman’s Function

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2238
Author(s):  
Rahul Goyal ◽  
Praveen Agarwal ◽  
Alexandra Parmentier ◽  
Clemente Cesarano
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Derivative Operator ◽  
The Family ◽  
Generating Relations ◽  
Fractional Derivative Operators ◽  
Extended Operator ◽  
Two Parameter

The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag–Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relationships with extended hypergeometric functions in order to derive this extended operator. Due to symmetry in the family of special functions, it is easy to study their various properties with the extended fractional derivative operators.

scholarly journals Gogolesque in the novel “The Life of Arseniev” by Ivan Bunin

2021 ◽  
Author(s):  
Elena Vranchan
Keyword(s):  
Point Of View ◽  
Small Scale ◽  
The Novel ◽  
Old World ◽  
The Past ◽  
The Family ◽  
Artistic Interpretation

The article deals with the peculiarities of the patriarchal noble-peasant life description in the novel “The Life of Arseniev” (1930) by Ivan Bunin, focuses on the use of characteristic Gogol’s images and techniques. Moreover, the comparison of the artistic interpretation ways of the patriarchal past by the writers reveals the Gogol's influence on the position of Bunin as the author, which is presented in the novel in different ways: from the point of view of an observer narrator who topographically accurately depicts the reality and life of the family estate, and from the point of view of an emigrant, focused on memories of the past, conveying an emotional sense of the connection between generations. In general, Bunin continues to develop the theme of the collision of immobile patriarchy with the quick movement of time that destroys the old serfdom, so his novel is imbued with nostalgia for the small-scale world going into the past. In Bunin's nostalgia, there are echoes of Gogol's sorrow about the doomed old world life.

scholarly journals On partly bilateral and partly unilateral generating functions

1986 ◽  
Vol 28 (2) ◽  
pp. 240-245 ◽  
Author(s):  
M. A. Pathan ◽  
Yasmeen
Keyword(s):  
Generating Functions ◽  
Laguerre Polynomials ◽  
Partial Derivatives ◽  
Starting Point ◽  
Generating Relations

AbstractThe purpose of this work is to begin the development of a theory of generating functions that will not only include the generating functions which are partly bilateral and partly unilateral but also provide a set of expansions, by taking successive partial derivatives with respect to one of the variables of the generating relations. Our starting point is a result of Exton [4] on associated Laguerre polynomials whose application gives certain generating functions of the polynomials of Jacobi and Appell, and functions of n variables of Lauricella.

scholarly journals Generalization of Konhauser Polynomials

2020 ◽  
Vol 2 (11) ◽  
pp. 8-14
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Biorthogonal System ◽  
Integral Representations ◽  
New Class ◽  
Generating Relations ◽  
Biorthogonal Polynomials

In this paper, we are showing study of biorthogonal polynomials associated with generalization of Laguere polynomials of Srivastava and Singhal [14]. It happens to generalized Konhauser. here we are trying to obtain the generating functions, recurrence relations, biorthogonality relations, integral representations and also bilinear and bilateral generating relations for the new class of biorthogonal system.

scholarly journals Reducibility of certain Kampé de Fériet function with an application to generating relations for products of two Laguerre polynomials

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 2059-2066
Author(s):  
Junesang Choi ◽  
Arjun Rathie
Keyword(s):  
Special Functions ◽  
Laguerre Polynomials ◽  
Research Subject ◽  
Single Form ◽  
Generating Relations ◽  
Summation Theorem

It has been an interesting and natural research subject to consider the reducibility of some extensively generalized special functions. In this regard, Kamp? de F?riet function has been attracted by many mathematicians. The authors [7] also established many interesting cases of the reducibility of Kamp? de F?riet function by employing generalizations of the two results for the terminating 2F1(2) hypergeometric identities due to Kim et al. In this sequel, we first aim at presenting several interesting cases of the reducibility of Kamp? de F?riet function by using generalizations of classical Kummer?s summation theorem due to Lavoie et al. We next show how one can use the above-given result to obtain eleven new generating relations for products of two Laguerre polynomials in a single-form result. We also consider many interesting and potentially useful specials cases of our main results.

scholarly journals Canines and carnassials as indicators of sociality in durophagous hyaenids: analyzing the past to understand the present

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e10541
Author(s):  
Juan Antonio Pérez-Claros ◽  
Carlos Coca-Ortega
Keyword(s):  
Principal Component ◽  
Point Of View ◽  
Crocuta Crocuta ◽  
The Past ◽  
Functional Aspects ◽  
Morphological Adaptations ◽  
Extant Species ◽  
The Family ◽  
Hyaena Hyaena ◽  
Multivariate Point

We analyzed the lower and upper dentition of the family Hyaenidae along its evolutionary history from a multivariate point of view. A total of 13,103 individual measurements of the lengths and widths of canines and the main post-canine teeth (lower third and fourth premolar, lower first molar, and upper second, third, and fourth premolars) were collected for 39 extinct and extant species of this family. We analyzed these measurements using principal component analyses. The multivariate structure characterized the main groups of previously defined hyaenid ecomorphs. Strikingly, our analyses also detected differences between social hunting durophages (such as Crocuta crocuta) and solitary scavengers (such as Hyaena hyaena or Parahyaena brunnea). Concerning the hyaenid bauplan, social hunters have large carnassials and smaller canines, whereas solitary scavengers show the exact opposite morphological adaptations. Additionally, scavengers exhibited upper canines larger than lower ones, whereas hunters have upper and lower canines of similar size. It is hypothesized that sociality has led to an increase in carnassial length for hunting durophages via scramble competition at feeding. Such competition also penalizes adults from bringing food to cubs, which are consequently breastfed. On the other hand, it is also hypothesized that natural selection has led to solitary scavengers having large canines to transport carcasses to cubs. Our results indicate that these functional aspects are also better reflected by lower teeth than the upper dentition, which leads to a mosaic evolution.

scholarly journals The time when the Mansi people kept the fire in a nāy sānyt ‘a box of fire’ (based on handwritten materials by P. E. Sheshkin)

2021 ◽  
Vol 11 (3) ◽  
pp. 556-562
Author(s):  
S. A. Popova ◽  
Keyword(s):  
Early Stage ◽  
Point Of View ◽  
Way Of Life ◽  
Historical Information ◽  
Ancient Time ◽  
The Past ◽  
A Value ◽  
The Family ◽  
Ethnic History ◽  
The Way

Introduction: the article is devoted to the study of religious ideas and events of one of the periods of the Mansi people’s life, which is designated by Sheshkin as nāy sānyt jis ‘the ancient time of fire [stored] in a box’. The article presents information about the family and public fire storage, construction of the box, the use of fire in different situations, its keepers. Ideas about fire are considered from the point of view of its personification (Fire-Mother, Fire-Woman); embodiment (it is alive, can talk, visit, revenge); mythologization (deity, special spirit of fire voytyl); object of veneration (holy mothers, dedication, sanctuaries). Folklore plots reflecting the ideas about «living» fire are revealed. Objective: to reconstruct the events and ideas of the northern Mansi group about fire in the era nāy sānyt jis. Research materials: handwritten texts of P. E. Sheshkin, published materials of the XIX–XXI centuries. Results and novelty of the research: the analysis reveals historical information on the way of life and organization of the Mansi during the period «the time when the Mansi kept fire in the nāy sānyt ‘box of fire’». The features of storing and using of family and collective fire are analyzed. The awareness of fire as a value is transmitted in the ideas of its supernatural essence, in the veneration of the Fire-Mother. The past fire, lost by people, is perceived as a super-fire (more powerful in brightness and heat, it lives together with a man and takes care of him). The attitude to fire as a shrine is reflected in the prohibitions, the dedication of it to animals (cat, frog), the construction of temples (sanctuaries). The novelty lies in the introduction into scientific circulation of the traditional ideas of the Mansi about the early stage of their ethnic history

Ethnology and the Study of Culture Change

Africa ◽  
1932 ◽  
Vol 5 (4) ◽  
pp. 383-392
Author(s):  
Fritz Krause
Keyword(s):  
Social Order ◽  
Point Of View ◽  
Economic Conditions ◽  
Cultural Life ◽  
Original Culture ◽  
The People ◽  
The Family ◽  
World Economic ◽  
High Degree ◽  
The Way

The ‘Five Year Plan of Research’ of the Institute described in this Journal, vol. v, no. 1, aims at a scientific study of the change in the cultural life of African peoples which, like an inevitable destiny, takes place under the influence of Western civilization. The object of the study is to provide a sound basis for dealing with practical questions of administration and education. Such an investigation must be based on an intensive knowledge of the original culture of the people to be studied; it must ascertain the foreign influences effecting the change, as well as the way in which they affect the culture of the people; and it has to study the changes being brought about by them in the culture. In order to start with concrete phenomena the investigation should, in the first instance, be confined to the changes that are being brought about by world economic conditions in the traditional social order of selected African communities, and in particular to the changes in the economic organization of native society. The study of changes in economic conditions must, however, inevitably lead to an examination of the way in which these affect the family, tribal organization, religious beliefs and sanctions, and the whole social organization. Regarded from the scientific point of view, this is a task which touches upon the most important problems of culture. Ethnology, as the most comprehensive and the most fundamental of the culturesciences, is to an especially high degree interested in this problem and in this investigation. Being myself a student of ethnology as a culturescience, I am venturing to discuss here the questions of principle involved, especially since the principles of culture-science underlying the ‘five year plan’ coincide to a large extent with my own conceptions.

scholarly journals Construction of a new family of Fubini-type polynomials and its applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
H. M. Srivastava ◽  
Rekha Srivastava ◽  
Abdulghani Muhyi ◽  
Ghazala Yasmin ◽  
Hibah Islahi ◽  
...  
Keyword(s):  
Generating Functions ◽  
Graphical Representation ◽  
Special Functions ◽  
Approximate Solutions ◽  
View Point ◽  
New Class ◽  
New Family ◽  
General Class Of Polynomials ◽  
Operational Technique ◽  
Derivative Formulas

AbstractThis paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introduce new families of special polynomials. Motivation of this paper is to construct a new class of generalized Fubini-type polynomials of the parametric kind via operational view point. The generating functions, differential equations, and other properties for these polynomials are established within the context of the monomiality principle. Using the generating functions, various interesting identities and relations related to the generalized Fubini-type polynomials are derived. Further, we obtain certain partial derivative formulas including the generalized Fubini-type polynomials. In addition, certain members belonging to the aforementioned general class of polynomials are considered. The numerical results to calculate the zeros and approximate solutions of these polynomials are given and their graphical representation are shown.

scholarly journals From special operators (1-Dx )n+α to Laguerre Polynomials

2021 ◽  
Vol 4 (3) ◽  
Keyword(s):  
Generating Functions ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Rodrigues Formula ◽  
Operator Calculus ◽  
Symbolic Formula ◽  
The Way

Laguerre polynomials Ln α (x) are shown to be the transforms of monomials by the special operators (1-Dx )n+α . From this their current properties such as Rodrigues formula, Lucas symbolic formula, orthogonality, generating functions, etc… are systematically obtained. This success opens the way for the study of special functions from special operators by the powerful operator calculus.

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