AbstractIn this paper, we consider the inverse Laplace transform of the Volterra μ-function (the Bromwich integral) and evaluate it with respect to the Hankel, Schläfli and Bourguet complex contours. In this sense, we establish the generalized Ramanujan's integral representations of the Volterra μ-function for general variations of the parameters. We also discuss the asymptotic analysis of this function with large parameters using the steepest descent method. Further, we show that the solution of Volterra integral equation with differentiated-order fractional integral operator is the Volterra μ-function.Keywords: Volterra μ-functionRamanujan's integralLaplace transformMathematics Subject Classifications: 41A6044A1045D05 AcknowledgmentsThe authors would like to acknowledge the reviewer for the helpful, constructive and encouraging comments.Disclosure statementNo potential conflict of interest was reported by the author(s).
摘要本文考虑Volterra μ-函数的拉普拉斯逆变换(Bromwich积分)，并在Hankel、Schläfli和Bourguet复轮廓上求值。在这种意义上，我们建立了参数一般变分的Volterra μ-函数的广义Ramanujan积分表示。我们还讨论了用最陡下降法对大参数函数的渐近分析。进一步证明了带微分阶分数阶积分算子的Volterra积分方程的解为Volterra μ函数。关键词:Volterra μ-functionRamanujan’s integra place transform数学学科分类:41A6044A1045D05致谢感谢审稿人提供的有益的、建设性的和鼓舞性的意见。披露声明作者未报告潜在的利益冲突。
{"title":"Generalization of the Ramanujan's integrals for the Volterra <i>μ</i> -functions via complex contours: representations and approximations","authors":"Arman Hashemzadeh Kalvari, Alireza Ansari, Hassan Askari","doi":"10.1080/10652469.2023.2260162","DOIUrl":"https://doi.org/10.1080/10652469.2023.2260162","url":null,"abstract":"AbstractIn this paper, we consider the inverse Laplace transform of the Volterra μ-function (the Bromwich integral) and evaluate it with respect to the Hankel, Schläfli and Bourguet complex contours. In this sense, we establish the generalized Ramanujan's integral representations of the Volterra μ-function for general variations of the parameters. We also discuss the asymptotic analysis of this function with large parameters using the steepest descent method. Further, we show that the solution of Volterra integral equation with differentiated-order fractional integral operator is the Volterra μ-function.Keywords: Volterra μ-functionRamanujan's integralLaplace transformMathematics Subject Classifications: 41A6044A1045D05 AcknowledgmentsThe authors would like to acknowledge the reviewer for the helpful, constructive and encouraging comments.Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136130074","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 : 2023-09-06DOI: 10.1080/10652469.2023.2255367
S. Atanasova, Snježana Maksimović, S. Pilipovic
{"title":"Abelian and Tauberian results for the fractional Fourier and short-time Fourier transforms of distributions","authors":"S. Atanasova, Snježana Maksimović, S. Pilipovic","doi":"10.1080/10652469.2023.2255367","DOIUrl":"https://doi.org/10.1080/10652469.2023.2255367","url":null,"abstract":"","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44808804","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 : 2023-08-30DOI: 10.1080/10652469.2023.2252977
O. Tyr, R. Daher
The problem of weighted integrability of the Fourier–Laguerre transform in terms of the moduli of smoothness related to generalized translations is considered. Sufficient conditions are given to solve this problem. These results generalize a famous Titchmarsh's theorem and Younis' theorem, due to Negzaoui in the Laguerre hypergroup. Also some results connected with the integrability of Fourier–Laguerre transforms of Laguerre convolutions are given.
{"title":"Sufficient conditions for the weighted integrability of Fourier–Laguerre transforms","authors":"O. Tyr, R. Daher","doi":"10.1080/10652469.2023.2252977","DOIUrl":"https://doi.org/10.1080/10652469.2023.2252977","url":null,"abstract":"The problem of weighted integrability of the Fourier–Laguerre transform in terms of the moduli of smoothness related to generalized translations is considered. Sufficient conditions are given to solve this problem. These results generalize a famous Titchmarsh's theorem and Younis' theorem, due to Negzaoui in the Laguerre hypergroup. Also some results connected with the integrability of Fourier–Laguerre transforms of Laguerre convolutions are given.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47181064","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 : 2023-08-18DOI: 10.1080/10652469.2023.2245118
J. Paneva-Konovska, Sarah A. Deif
In this paper, some properties related to the -parametric Mittag-Leffler (M-L) functions are investigated. More precisely, three families of such functions with different kinds of indices are examined. Appropriate estimates and asymptotic formulae are obtained and which are further used in proving the convergence of series of functions of these families in the whole complex plane, as well as in its compact subsets. Using these auxiliary results, different relations referring to the discussed families are obtained; generalizing the ones already known for particular cases of the parameters. Those are considered different representations of the -parametric M-L functions pertaining to the families discussed, and with which various equalities are established relating different sums that involve matrix coefficients. Some interesting properties are reached for particular choices of the matrices. Finally, bounds of the -parametric M-L function are given under a perturbed matrix argument.
{"title":"On some relations in the class of multi-index Mittag-Leffler functions","authors":"J. Paneva-Konovska, Sarah A. Deif","doi":"10.1080/10652469.2023.2245118","DOIUrl":"https://doi.org/10.1080/10652469.2023.2245118","url":null,"abstract":"In this paper, some properties related to the -parametric Mittag-Leffler (M-L) functions are investigated. More precisely, three families of such functions with different kinds of indices are examined. Appropriate estimates and asymptotic formulae are obtained and which are further used in proving the convergence of series of functions of these families in the whole complex plane, as well as in its compact subsets. Using these auxiliary results, different relations referring to the discussed families are obtained; generalizing the ones already known for particular cases of the parameters. Those are considered different representations of the -parametric M-L functions pertaining to the families discussed, and with which various equalities are established relating different sums that involve matrix coefficients. Some interesting properties are reached for particular choices of the matrices. Finally, bounds of the -parametric M-L function are given under a perturbed matrix argument.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45682441","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 : 2023-08-11DOI: 10.1080/10652469.2023.2244648
O. Kouba
ABSTRACT Using the Fourier–Gegenbauer series, we prove several identities that generalize known results. In particular, it is proved, that for all complex numbers such that and . In addition, for all nonnegative integers m, we obtain the Ramanujan-type series Which are known in the case m=0.
{"title":"Binomial identities obtained from the Gegenbauer series expansion","authors":"O. Kouba","doi":"10.1080/10652469.2023.2244648","DOIUrl":"https://doi.org/10.1080/10652469.2023.2244648","url":null,"abstract":"ABSTRACT Using the Fourier–Gegenbauer series, we prove several identities that generalize known results. In particular, it is proved, that for all complex numbers such that and . In addition, for all nonnegative integers m, we obtain the Ramanujan-type series Which are known in the case m=0.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49446859","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 : 2023-08-09DOI: 10.1080/10652469.2023.2243667
Haipan Shi, Heju Yang, Y. Qiao
ABSTRACT In this paper, we establish a Riemann–Lebesgue theorem and some real Paley–Wiener-type theorems for the fractional Clifford–Fourier transform (FrCFT). Furthermore, because of the non-commutativity of Clifford algebra, we study some basic properties from linearity to modulation of the FrCFT about the left-multiplied functions and the right-multiplied functions.
{"title":"Properties of the fractional Clifford–Fourier transform","authors":"Haipan Shi, Heju Yang, Y. Qiao","doi":"10.1080/10652469.2023.2243667","DOIUrl":"https://doi.org/10.1080/10652469.2023.2243667","url":null,"abstract":"ABSTRACT In this paper, we establish a Riemann–Lebesgue theorem and some real Paley–Wiener-type theorems for the fractional Clifford–Fourier transform (FrCFT). Furthermore, because of the non-commutativity of Clifford algebra, we study some basic properties from linearity to modulation of the FrCFT about the left-multiplied functions and the right-multiplied functions.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45967477","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 : 2023-08-07DOI: 10.1080/10652469.2023.2238241
Yu. A. Brychkov, N. Savischenko
{"title":"On some formulas for the confluent Horn functions H10(c) (a; c; w, z) and H11(c) (a, c, c′; d; w, z)","authors":"Yu. A. Brychkov, N. Savischenko","doi":"10.1080/10652469.2023.2238241","DOIUrl":"https://doi.org/10.1080/10652469.2023.2238241","url":null,"abstract":"","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45575840","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 : 2023-07-21DOI: 10.1080/10652469.2023.2238115
S. Alexanian, A. Kuznetsov
We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function G(z;τ). Second, we ...
{"title":"On the Barnes double gamma function","authors":"S. Alexanian, A. Kuznetsov","doi":"10.1080/10652469.2023.2238115","DOIUrl":"https://doi.org/10.1080/10652469.2023.2238115","url":null,"abstract":"We aim to achieve the following three goals. First of all, we collect all known definitions, transformation properties and functional identities of Barnes double gamma function G(z;τ). Second, we ...","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"542 ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138519624","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 : 2023-07-11DOI: 10.1080/10652469.2023.2234556
Chelo Ferreira, J. López, Ester Pérez Sinusía
The -function of communication theory plays an important role in the error rate analysis in digital communication with the presence of additive white Gaussian noise (AWGN) and generalized multipath fading conditions. In this paper we investigate several convergent and/or asymptotic expansions of for some limiting values of their variables and parameters: large values of z, large values of p, small values of η, and values of . We provide explicit and/or recursive algorithms for the computation of the coefficients of the expansions. Some numerical examples illustrate the accuracy of the approximations.
{"title":"New series expansions for the -function of communication theory","authors":"Chelo Ferreira, J. López, Ester Pérez Sinusía","doi":"10.1080/10652469.2023.2234556","DOIUrl":"https://doi.org/10.1080/10652469.2023.2234556","url":null,"abstract":"The -function of communication theory plays an important role in the error rate analysis in digital communication with the presence of additive white Gaussian noise (AWGN) and generalized multipath fading conditions. In this paper we investigate several convergent and/or asymptotic expansions of for some limiting values of their variables and parameters: large values of z, large values of p, small values of η, and values of . We provide explicit and/or recursive algorithms for the computation of the coefficients of the expansions. Some numerical examples illustrate the accuracy of the approximations.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46888817","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 : 2023-07-03DOI: 10.1080/10652469.2023.2230610
N. M. Khoa
The main aim of this work is to establish a new polyconvolution operator with the weight function for the Hartley integral transforms. After that, we will apply it to solve some classes of integral equations and a system of integral equations of polyconvolution type. On the other hand, we study the Wastson-type integral transform for this polyconvolution. We establish necessary and sufficient conditions for these operators to be unitary in the space and get their inverse represented in the conjugate symmetric form. Furthermore, we also formulate the Placherel-type theorem for the aforementioned operators, prove a sequence of functions that converges to the original function in the norm of , and further show the boundedness of these operators.
{"title":"On the polyconvolution operator with a trigonometric weight function for the Hartley integral transforms and applications","authors":"N. M. Khoa","doi":"10.1080/10652469.2023.2230610","DOIUrl":"https://doi.org/10.1080/10652469.2023.2230610","url":null,"abstract":"The main aim of this work is to establish a new polyconvolution operator with the weight function for the Hartley integral transforms. After that, we will apply it to solve some classes of integral equations and a system of integral equations of polyconvolution type. On the other hand, we study the Wastson-type integral transform for this polyconvolution. We establish necessary and sufficient conditions for these operators to be unitary in the space and get their inverse represented in the conjugate symmetric form. Furthermore, we also formulate the Placherel-type theorem for the aforementioned operators, prove a sequence of functions that converges to the original function in the norm of , and further show the boundedness of these operators.","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"861 - 877"},"PeriodicalIF":1.0,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43878500","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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