Volume 31, Issue 4
On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation

Anal. Theory Appl., 31 (2015), pp. 407-420.

Published online: 2017-10

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• Abstract

In the present paper, we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of ${E_n}( {F,\beta } )$ where ${E_n}( {F,\beta } )$ is the error in approximating of the function $F(s)$  by definite integral polynomials in the half plane ${{Re}} s \le \beta < \alpha.$

• Keywords

Laplace-Stieltjes transformation, analytic function, order, type, approximation error.

30D15, 32A15

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@Article{ATA-31-407, author = {}, title = {On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {4}, pages = {407--420}, abstract = {

In the present paper, we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of ${E_n}( {F,\beta } )$ where ${E_n}( {F,\beta } )$ is the error in approximating of the function $F(s)$  by definite integral polynomials in the half plane ${{Re}} s \le \beta < \alpha.$

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n4.6}, url = {http://global-sci.org/intro/article_detail/ata/4648.html} }
TY - JOUR T1 - On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation JO - Analysis in Theory and Applications VL - 4 SP - 407 EP - 420 PY - 2017 DA - 2017/10 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n4.6 UR - https://global-sci.org/intro/article_detail/ata/4648.html KW - Laplace-Stieltjes transformation, analytic function, order, type, approximation error. AB -

In the present paper, we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of ${E_n}( {F,\beta } )$ where ${E_n}( {F,\beta } )$ is the error in approximating of the function $F(s)$  by definite integral polynomials in the half plane ${{Re}} s \le \beta < \alpha.$

G. S. Srivastava & Ch. Singhal. (1970). On the Approximation of an Analytic Function Represented by Laplace-Stieltjes Transformation. Analysis in Theory and Applications. 31 (4). 407-420. doi:10.4208/ata.2015.v31.n4.6
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