{"title":"Identities for combinatorial sums involving trigonometric functions","authors":"H. Alzer, S. Yakubovich","doi":"10.1080/10652469.2023.2172004","DOIUrl":"https://doi.org/10.1080/10652469.2023.2172004","url":null,"abstract":"Let and where and are integers and a is a real number. We present two proofs for the following results: If , then If , then . If , then If , then .","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"563 - 569"},"PeriodicalIF":1.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46407794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-29DOI: 10.1080/10652469.2022.2155642
A. J. Durán, Mónica Rueda
Meixner type polynomials are defined from the Meixner polynomials by using Casoratian determinants whose entries belong to two given finite sets of polynomials and . They are eigenfunctions of higher-order difference operators but only for a careful choice of the polynomials and , the sequence is orthogonal with respect to a measure. Under mild assumptions, we characterize in this paper the algebra formed by all difference operators with respect to which the family of Meixner type polynomials are eigenfunctions.
{"title":"The algebra of difference operators associated to Meixner type polynomials","authors":"A. J. Durán, Mónica Rueda","doi":"10.1080/10652469.2022.2155642","DOIUrl":"https://doi.org/10.1080/10652469.2022.2155642","url":null,"abstract":"Meixner type polynomials are defined from the Meixner polynomials by using Casoratian determinants whose entries belong to two given finite sets of polynomials and . They are eigenfunctions of higher-order difference operators but only for a careful choice of the polynomials and , the sequence is orthogonal with respect to a measure. Under mild assumptions, we characterize in this paper the algebra formed by all difference operators with respect to which the family of Meixner type polynomials are eigenfunctions.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"503 - 521"},"PeriodicalIF":1.0,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42326712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-26DOI: 10.1080/10652469.2022.2159959
L. Khériji, K. Omrani
In the present work, we deal with a monic orthogonal polynomial sequence (MOPS) deduced by its cubic decomposition (CD) . Our goal is to determine all D-Laguerre–Hahn strict of class one of these sequences. From the CD structure, only one family of MOPS appears in connection with the D-Laguerre–Hahn of class zero of Jacobi type in the singular case and the nonsingular one. Their recurrence coefficients are highlighted.
{"title":"Characterization of the D-Laguerre–Hahn orthogonal polynomials of class one via the cubic decomposition","authors":"L. Khériji, K. Omrani","doi":"10.1080/10652469.2022.2159959","DOIUrl":"https://doi.org/10.1080/10652469.2022.2159959","url":null,"abstract":"In the present work, we deal with a monic orthogonal polynomial sequence (MOPS) deduced by its cubic decomposition (CD) . Our goal is to determine all D-Laguerre–Hahn strict of class one of these sequences. From the CD structure, only one family of MOPS appears in connection with the D-Laguerre–Hahn of class zero of Jacobi type in the singular case and the nonsingular one. Their recurrence coefficients are highlighted.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"570 - 588"},"PeriodicalIF":1.0,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41363774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-24DOI: 10.1080/10652469.2022.2155956
C. Chettaoui, Amina Hassini, K. Trimèche
{"title":"Quantitative uncertainty principles for the Gabor spherical mean transform","authors":"C. Chettaoui, Amina Hassini, K. Trimèche","doi":"10.1080/10652469.2022.2155956","DOIUrl":"https://doi.org/10.1080/10652469.2022.2155956","url":null,"abstract":"","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43178642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-24DOI: 10.1080/10652469.2022.2157414
T. Pogány, N. Laraqi
The main aim of this article is to establish a closed-form expression for the Neumann series built with Macdonald functions in which order contains the summation index and the coefficients include the summation index exponentially and factorially. Motivated by this problem which occurs in several problems of physics or electrochemistry such as diffusion phenomena, we derive two integral representations of a general Neumann series of this type containing Macdonald functions as building blocks.
{"title":"On Neumann series of Macdonald functions","authors":"T. Pogány, N. Laraqi","doi":"10.1080/10652469.2022.2157414","DOIUrl":"https://doi.org/10.1080/10652469.2022.2157414","url":null,"abstract":"The main aim of this article is to establish a closed-form expression for the Neumann series built with Macdonald functions in which order contains the summation index and the coefficients include the summation index exponentially and factorially. Motivated by this problem which occurs in several problems of physics or electrochemistry such as diffusion phenomena, we derive two integral representations of a general Neumann series of this type containing Macdonald functions as building blocks.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"552 - 561"},"PeriodicalIF":1.0,"publicationDate":"2022-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42341961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-22DOI: 10.1080/10652469.2022.2155643
J. Hindmarsh, M. C. Lettington
In this present work polynomial transformations are identified that preserve the property of the polynomials having all zeros lying on the imaginary axis. Existence results concerning families of polynomials whose generalized Mellin transforms have zeros all lying on the critical line are then derived. Inherent structures are identified from which a simple proof relating to the Gegenbauer family of orthogonal polynomials is subsequently deduced. Some discussion about the choice of generalized Mellin transform is also given.
{"title":"On polynomial transformations preserving purely imaginary zeros*","authors":"J. Hindmarsh, M. C. Lettington","doi":"10.1080/10652469.2022.2155643","DOIUrl":"https://doi.org/10.1080/10652469.2022.2155643","url":null,"abstract":"In this present work polynomial transformations are identified that preserve the property of the polynomials having all zeros lying on the imaginary axis. Existence results concerning families of polynomials whose generalized Mellin transforms have zeros all lying on the critical line are then derived. Inherent structures are identified from which a simple proof relating to the Gegenbauer family of orthogonal polynomials is subsequently deduced. Some discussion about the choice of generalized Mellin transform is also given.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"522 - 536"},"PeriodicalIF":1.0,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43816156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-15DOI: 10.1080/10652469.2022.2155819
Miao-Kun Wang, Zai-Yin He, Tie-hong Zhao, Qi Bao
ABSTRACT This paper deals with the complete integral of the second kind approximated by the weighted Hölder mean. In general, there are two ways to be considered. One is to find the best exponential parameters with a given weight, and the other is to find the optimal weights with a given exponential order. The second method will be used in this paper where we find the sharp weighted Hölder mean bounds for in a sense of weight. As a result, we also provide a new method to find the optimal Hölder mean bounds for .
{"title":"Sharp weighted Hölder mean bounds for the complete elliptic integral of the second kind","authors":"Miao-Kun Wang, Zai-Yin He, Tie-hong Zhao, Qi Bao","doi":"10.1080/10652469.2022.2155819","DOIUrl":"https://doi.org/10.1080/10652469.2022.2155819","url":null,"abstract":"ABSTRACT This paper deals with the complete integral of the second kind approximated by the weighted Hölder mean. In general, there are two ways to be considered. One is to find the best exponential parameters with a given weight, and the other is to find the optimal weights with a given exponential order. The second method will be used in this paper where we find the sharp weighted Hölder mean bounds for in a sense of weight. As a result, we also provide a new method to find the optimal Hölder mean bounds for .","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"537 - 551"},"PeriodicalIF":1.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45956044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-05DOI: 10.1080/10652469.2022.2152812
S. Platonov
In various sections of the classical Fourier Analysis, the problem of the convergence of the integrals as and under various assumptions on the functions f and g are considered. In this paper, we study some analogues of such problems for weight integrals of the form for functions f and g from some weighted functional classes that are connected with Fourier–Bessel harmonic analysis.
{"title":"Limits of some integrals connected with Bessel analysis","authors":"S. Platonov","doi":"10.1080/10652469.2022.2152812","DOIUrl":"https://doi.org/10.1080/10652469.2022.2152812","url":null,"abstract":"In various sections of the classical Fourier Analysis, the problem of the convergence of the integrals as and under various assumptions on the functions f and g are considered. In this paper, we study some analogues of such problems for weight integrals of the form for functions f and g from some weighted functional classes that are connected with Fourier–Bessel harmonic analysis.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"495 - 502"},"PeriodicalIF":1.0,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48711166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-30DOI: 10.1080/10652469.2022.2149746
Marta Na Chen, W. Chu
By employing the linearization method and partial fractions, we examine a large class of nonterminating exotic -series extended by five integer parameters. A general summation formula is proved, and several contiguous series are evaluated in closed form.
{"title":"Contiguous values for a class of nonterminating 3F2(1)-series","authors":"Marta Na Chen, W. Chu","doi":"10.1080/10652469.2022.2149746","DOIUrl":"https://doi.org/10.1080/10652469.2022.2149746","url":null,"abstract":"By employing the linearization method and partial fractions, we examine a large class of nonterminating exotic -series extended by five integer parameters. A general summation formula is proved, and several contiguous series are evaluated in closed form.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"457 - 468"},"PeriodicalIF":1.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48969792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-30DOI: 10.1080/10652469.2022.2150764
Rekha Meena, Ajit Kumar Bhabor
The aim of this article is to define the bicomplex hypergeometric function. We obtain some useful results from the theory of special functions over a relatively large domain. We discuss the bicomplex holomorphicity of the bicomplex hypergeometric function and establish some significant relations based on it along with some bicomplex geometric representations of conditions of existence.
{"title":"Bicomplex hypergeometric function and its properties","authors":"Rekha Meena, Ajit Kumar Bhabor","doi":"10.1080/10652469.2022.2150764","DOIUrl":"https://doi.org/10.1080/10652469.2022.2150764","url":null,"abstract":"The aim of this article is to define the bicomplex hypergeometric function. We obtain some useful results from the theory of special functions over a relatively large domain. We discuss the bicomplex holomorphicity of the bicomplex hypergeometric function and establish some significant relations based on it along with some bicomplex geometric representations of conditions of existence.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"478 - 494"},"PeriodicalIF":1.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41512046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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