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New interesting Euler sums 新的有趣的欧拉和
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-15-02
A. Nimbran, A. Sofo
{"title":"New interesting Euler sums","authors":"A. Nimbran, A. Sofo","doi":"10.7153/jca-2019-15-02","DOIUrl":"https://doi.org/10.7153/jca-2019-15-02","url":null,"abstract":". We present here some new and interesting Euler sums obtained by means of related integrals and elementary approach. We supplement Euler’s general recurrence formula with two general formulas of the form ∑ n (cid:2) 1 O ( m ) n (cid:2) 1 ( 2 n − 1 ) p + 1 ( 2 n ) p (cid:3) and ∑ n (cid:2) 1 O n ( 2 n − 1 ) p ( 2 n + 1 ) q , where O ( m ) n = n ∑ j = 1 1 ( 2 j − 1 ) m . Two formulas for ζ ( 5 ) are also derived.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Further results about normal criteria and shared values for families of meromorphic functions 亚纯函数族的正规准则和共享值的进一步结果
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/JCA-2019-14-06
Jianm ng Qi
{"title":"Further results about normal criteria and shared values for families of meromorphic functions","authors":"Jianm ng Qi","doi":"10.7153/JCA-2019-14-06","DOIUrl":"https://doi.org/10.7153/JCA-2019-14-06","url":null,"abstract":". Let k be a positive integer and let F be a family of meromorphic functions in the domain D all of whose zeros with multiplicity at least k . Let P be a polynomial and P have at least one simple zero, p = deg ( P ) (cid:2) k + 2. If, for each pair f , g ∈ F , P ( f ) G m ( f ) and P ( g ) G m ( g ) share a nonzero constant b ignoring multiplicity in D, where G ( f ) = P ( f ( k ) )+ H ( f ) is a differential polynomial of f satisfying w deg | H (cid:3) kmql + mq + 1 or w ( H ) − deg ( H ) < qk , and q > l (cid:2) k + 1 is a positive integer, then F is normal in D.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
2D-Sheffer-Mittag-Leffler polynomials: properties and examples 2D-Sheffer-Mittag-Leffler多项式:性质和例子
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-15-10
Subuhi Khan, Mahvish Ali, Shakeel Ahmad Naikoo
{"title":"2D-Sheffer-Mittag-Leffler polynomials: properties and examples","authors":"Subuhi Khan, Mahvish Ali, Shakeel Ahmad Naikoo","doi":"10.7153/jca-2019-15-10","DOIUrl":"https://doi.org/10.7153/jca-2019-15-10","url":null,"abstract":"In this work, the 2D-Sheffer polynomials and the Mittag-Leffler polynomials are combined to introduce the family of the 2D-Sheffer-Mittag-Leffler polynomials. The generating function, quasi-monomial properties and series definition of these polynomials are established. Examples of some members belonging to this family are considered. The graphs of some hybrid special polynomials are also drawn for suitable values of the indices. Mathematics subject classification (2010): 33C45, 33C99, 33E20.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On theorems connecting Mellin and Hankel transforms 关于连接Mellin变换和Hankel变换的定理
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-15-12
Viren ra Kumar
{"title":"On theorems connecting Mellin and Hankel transforms","authors":"Viren ra Kumar","doi":"10.7153/jca-2019-15-12","DOIUrl":"https://doi.org/10.7153/jca-2019-15-12","url":null,"abstract":"","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71135371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Further investigations on some results of Yu 对余部分结果的进一步调查
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/JCA-2019-14-01
A. Banerjee, M. B. Ahamed
{"title":"Further investigations on some results of Yu","authors":"A. Banerjee, M. B. Ahamed","doi":"10.7153/JCA-2019-14-01","DOIUrl":"https://doi.org/10.7153/JCA-2019-14-01","url":null,"abstract":". With the help of weighted sharing of values, we investigate the uniqueness of rational function of a meromorphic functions sharing a small function with its differential polynomial. Our results will extend and improve a number of result in the direction of Yu [18]. Speci fi cally we stress on the improvement of two recent results of Charak and Lal [8] and Li, Yang and Liu [14]. We have exhibited several examples to justify our certain claims.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Schur's theorem for modified discrete Fourier transform 修正离散傅里叶变换的舒尔定理
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-15-07
N. O. Kotelina, A. B. Pevnyi
{"title":"Schur's theorem for modified discrete Fourier transform","authors":"N. O. Kotelina, A. B. Pevnyi","doi":"10.7153/jca-2019-15-07","DOIUrl":"https://doi.org/10.7153/jca-2019-15-07","url":null,"abstract":"Abstract. We find the eigenvalues of modified Fourier matrix S with entries Sk j = 1 √n ω k(1− j) , 0 k, j n− 1 , where ω = exp 2πi n . For this matrix S4 = ωI . The matrix has an interesting property: for n = 4m eigenvalues have equal multiplicities. We prove a theorem giving the multiplicities of eigenvalues for all n . The theorem is similar to Schur’s theorem (1921) for standard Fourier matrix. Our proofs are self-contained. In the proof we calculate modified Gauss sums by means of the classical analysis.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A bounds Tauberian theorem 一个有界的陶伯利定理
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-15-04
A. Stenger
{"title":"A bounds Tauberian theorem","authors":"A. Stenger","doi":"10.7153/jca-2019-15-04","DOIUrl":"https://doi.org/10.7153/jca-2019-15-04","url":null,"abstract":". We weaken the hypothesis and the conclusion of a Hardy–Littlewood Tauberian the- orem, and apply the new theorem to deduce asymptotic behavior of the coef fi cients of an expo-nentiated lacunary series.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Four dimensional logarithmic transformation into ℒ_u 四维对数变换成的函数
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/JCA-2019-14-05
F. Nuray, N. P. Akin
{"title":"Four dimensional logarithmic transformation into ℒ_u","authors":"F. Nuray, N. P. Akin","doi":"10.7153/JCA-2019-14-05","DOIUrl":"https://doi.org/10.7153/JCA-2019-14-05","url":null,"abstract":". Let t = ( t m ) and t = ( t n ) be two null sequences in the interval ( 0 , 1 ) and de fi ne the four dimensional logarithmic matrix L t , t = ( by The matrix L determines a sequence -to-sequence variant of classicial logarithmic summabil- ity method. The aim of this paper is to study these transformations to be L u − L u summability methods.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coupon collector's problem with unlike probabilities 优惠券收集者的问题与不同的概率
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/JCA-2019-14-13
Toshio Nakata
{"title":"Coupon collector's problem with unlike probabilities","authors":"Toshio Nakata","doi":"10.7153/JCA-2019-14-13","DOIUrl":"https://doi.org/10.7153/JCA-2019-14-13","url":null,"abstract":"In this note we study the coupon collector’s problem with unlike probabilities using majorization and a Schur concave function.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Bounds on coefficients and third Hankel determinant for a class of analytic functions related with certain conic domain 一类与某二次域有关的解析函数的系数界和第三次汉克尔行列式
Journal of classical analysis Pub Date : 2019-01-01 DOI: 10.7153/jca-2019-15-06
J. K. Prajapat, Rajbala
{"title":"Bounds on coefficients and third Hankel determinant for a class of analytic functions related with certain conic domain","authors":"J. K. Prajapat, Rajbala","doi":"10.7153/jca-2019-15-06","DOIUrl":"https://doi.org/10.7153/jca-2019-15-06","url":null,"abstract":"In this paper, we obtain upper bounds on initial coefficients and third Hankel determinant H3,1( f ) = ∣ ∣ ∣ ∣ ∣ ∣ a1 a2 a3 a2 a3 a4 a3 a4 a5 ∣ ∣ ∣ ∣ ∣ ∣ of the coefficients of analytic function f (z) = z + a2z + a3z + · · · , belonging to the class S ∗(q) in the open unit disk D , which satisfies the subordination condition that z f ′(z)/ f (z) ≺ q(z) (z ∈ D), where q(z) = √ 1+ z2 +z . Several results are presented exhibiting improvement in earlier work. Mathematics subject classification (2010): 30C45.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71134954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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