Pub Date : 2024-09-08DOI: 10.1080/10652469.2024.2399520
Esra Güldoğan Lekesız, Bayram Çekım
In this paper, some new families of biorthogonal functions in one variable produced by using Fourier transforms of biorthogonal polynomials, which are suggested by Laguerre, Jacobi and Szegö–Hermit...
{"title":"Fourier transform of biorthogonal polynomials in one variable*","authors":"Esra Güldoğan Lekesız, Bayram Çekım","doi":"10.1080/10652469.2024.2399520","DOIUrl":"https://doi.org/10.1080/10652469.2024.2399520","url":null,"abstract":"In this paper, some new families of biorthogonal functions in one variable produced by using Fourier transforms of biorthogonal polynomials, which are suggested by Laguerre, Jacobi and Szegö–Hermit...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"54 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221745","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 : 2024-09-08DOI: 10.1080/10652469.2024.2400698
Wen-Biao Gao
In this paper, we obtain the convolution theorems for the windowed linear canonical transform (WLCT). According to the WLCT of a convolution of two functions is the product of their respective WLCT...
{"title":"Convolution theorem for the windowed linear canonical transform","authors":"Wen-Biao Gao","doi":"10.1080/10652469.2024.2400698","DOIUrl":"https://doi.org/10.1080/10652469.2024.2400698","url":null,"abstract":"In this paper, we obtain the convolution theorems for the windowed linear canonical transform (WLCT). According to the WLCT of a convolution of two functions is the product of their respective WLCT...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"18 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221743","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 : 2024-08-23DOI: 10.1080/10652469.2024.2392281
Chen Hai-sheng, Zhu Ye-cheng
In this paper, we prove that the inequalities Hp(K(r),E(r))<π2,Lq(K(r),E(r))<π2 hold for all r∈(0,1) if and only if p≤−log3/log(π/2) and q<−1, where Hp(a,b) and Lq(a,b) are respectively the p-th...
{"title":"Optimal power-type Heronian and Lehmer means inequalities for the complete elliptic integrals","authors":"Chen Hai-sheng, Zhu Ye-cheng","doi":"10.1080/10652469.2024.2392281","DOIUrl":"https://doi.org/10.1080/10652469.2024.2392281","url":null,"abstract":"In this paper, we prove that the inequalities Hp(K(r),E(r))<π2,Lq(K(r),E(r))<π2 hold for all r∈(0,1) if and only if p≤−log3/log(π/2) and q<−1, where Hp(a,b) and Lq(a,b) are respectively the p-th...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262900","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 : 2024-08-08DOI: 10.1080/10652469.2024.2389539
Khalfa Douak
We investigate the symmetric Dunkl-classical orthogonal polynomials by using a new approach in connection with the Dunkl operator. The main aim of this technique is first and foremost to determine ...
{"title":"The symmetric Dunkl-classical orthogonal polynomials revisited","authors":"Khalfa Douak","doi":"10.1080/10652469.2024.2389539","DOIUrl":"https://doi.org/10.1080/10652469.2024.2389539","url":null,"abstract":"We investigate the symmetric Dunkl-classical orthogonal polynomials by using a new approach in connection with the Dunkl operator. The main aim of this technique is first and foremost to determine ...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937628","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 : 2024-08-05DOI: 10.1080/10652469.2024.2387752
Mohannad J. S. Shahwan, Maged G. Bin-Saad
The goal of this research is to present and investigate a novel class of 2D-Laguerre polynomials, which contains some well-known 2D-polynomials as special cases.We discuss its numerous features, in...
这项研究的目的是提出并研究一类新的二维-拉盖尔多项式，其中包含一些著名的二维多项式特例。
{"title":"Generalized form of 2D-Laguerre polynomials","authors":"Mohannad J. S. Shahwan, Maged G. Bin-Saad","doi":"10.1080/10652469.2024.2387752","DOIUrl":"https://doi.org/10.1080/10652469.2024.2387752","url":null,"abstract":"The goal of this research is to present and investigate a novel class of 2D-Laguerre polynomials, which contains some well-known 2D-polynomials as special cases.We discuss its numerous features, in...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"6 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937621","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 : 2024-08-01DOI: 10.1080/10652469.2024.2382810
A. V. Grishaev, V. F. Sazonov
The work proposes new formulas for Maclaurin's series expansions of natural and real powers of the arctangent and hyperbolic arctangent, a new explicit formula for the Meixner polynomial of the sec...
{"title":"New formulas for Maclaurin's series expansions of powers of arctangent and other related topics","authors":"A. V. Grishaev, V. F. Sazonov","doi":"10.1080/10652469.2024.2382810","DOIUrl":"https://doi.org/10.1080/10652469.2024.2382810","url":null,"abstract":"The work proposes new formulas for Maclaurin's series expansions of natural and real powers of the arctangent and hyperbolic arctangent, a new explicit formula for the Meixner polynomial of the sec...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"132 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937623","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 : 2024-07-31DOI: 10.1080/10652469.2024.2379529
Yu. A. Brychkov
Properties of the Lommel polynomials Rn,ν(z) which appear in the theory of the Bessel functions, are studied. New functional relations for hypergeometric and Horn functions, including reduction for...
{"title":"The Lommel polynomials and related formulas","authors":"Yu. A. Brychkov","doi":"10.1080/10652469.2024.2379529","DOIUrl":"https://doi.org/10.1080/10652469.2024.2379529","url":null,"abstract":"Properties of the Lommel polynomials Rn,ν(z) which appear in the theory of the Bessel functions, are studied. New functional relations for hypergeometric and Horn functions, including reduction for...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"30 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937622","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 : 2024-07-30DOI: 10.1080/10652469.2024.2386664
Jeetendrasingh Maan, E. R. Negrín
This paper aims to derive Parseval-Goldstein type relations for the index Whittaker transform. Additionally, the study explores the continuity properties of both the index Whittaker transform and i...
{"title":"Parseval-Goldstein type theorems for the index Whittaker transform","authors":"Jeetendrasingh Maan, E. R. Negrín","doi":"10.1080/10652469.2024.2386664","DOIUrl":"https://doi.org/10.1080/10652469.2024.2386664","url":null,"abstract":"This paper aims to derive Parseval-Goldstein type relations for the index Whittaker transform. Additionally, the study explores the continuity properties of both the index Whittaker transform and i...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"185 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227280","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 : 2024-07-17DOI: 10.1080/10652469.2024.2378830
Aydin Behnad
A novel integral identity is introduced that can be applied to circular and diamond symmetric functions. It is demonstrated how this new identity and its alternative representations can be employed...
{"title":"A novel integral identity for circular and diamond symmetric functions","authors":"Aydin Behnad","doi":"10.1080/10652469.2024.2378830","DOIUrl":"https://doi.org/10.1080/10652469.2024.2378830","url":null,"abstract":"A novel integral identity is introduced that can be applied to circular and diamond symmetric functions. It is demonstrated how this new identity and its alternative representations can be employed...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"203 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744741","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 : 2024-07-17DOI: 10.1080/10652469.2024.2381148
F. Bouzeffour
This paper introduces an innovative fractional multidimensional Bessel transform, enhanced by a novel convolution structure. This integral transform parallels the established roles of the Fourier a...
{"title":"The fractional multi-dimensional Bessel transform and its role in anisotropic Riesz-Bessel potential","authors":"F. Bouzeffour","doi":"10.1080/10652469.2024.2381148","DOIUrl":"https://doi.org/10.1080/10652469.2024.2381148","url":null,"abstract":"This paper introduces an innovative fractional multidimensional Bessel transform, enhanced by a novel convolution structure. This integral transform parallels the established roles of the Fourier a...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744742","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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