Solution of Singular Integral Equations of the First Kind with Cauchy Kernel
In this paper an analytic method is developed for solving Cauchy type singular integral equations of the first kind, over a finite interval. Chebyshev polynomials of the first kind, $T_n(x)$, second kind, $U_n(x)$, third kind, $V_n(x)$, and fourth kind, $W_n(x)$, corresponding to respective weight f...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2019-03-01
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| Series: | Communications in Advanced Mathematical Sciences |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/677061 |
| _version_ | 1797294242337390592 |
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| author | B.n. Mandal Subhabrata Mondal |
| author_facet | B.n. Mandal Subhabrata Mondal |
| author_sort | B.n. Mandal |
| collection | DOAJ |
| description | In this paper an analytic method is developed for solving Cauchy type singular integral equations of the first kind, over a finite interval. Chebyshev polynomials of the first kind, $T_n(x)$, second kind, $U_n(x)$, third kind, $V_n(x)$, and fourth kind, $W_n(x)$, corresponding to respective weight functions $W^{(1)}(x)=\frac{1}{\sqrt{1-x^2}},W^{(2)}(x)=\sqrt{1-x^2},W^{(3)}(x)=\sqrt{\frac{1+x}{1-x}},$ and $~ W^{(3)}(x)=\sqrt{\frac{1-x}{1+x}}, $ have been used to obtain the complete analytical solutions for four different cases. |
| first_indexed | 2024-03-07T21:27:24Z |
| format | Article |
| id | doaj.art-fe28ccb9e9b2407d8585fe67df4d3566 |
| institution | Directory Open Access Journal |
| issn | 2651-4001 |
| language | English |
| last_indexed | 2024-03-07T21:27:24Z |
| publishDate | 2019-03-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Communications in Advanced Mathematical Sciences |
| spelling | doaj.art-fe28ccb9e9b2407d8585fe67df4d35662024-02-27T04:36:36ZengEmrah Evren KARACommunications in Advanced Mathematical Sciences2651-40012019-03-0121697410.33434/cams.4547401225Solution of Singular Integral Equations of the First Kind with Cauchy KernelB.n. Mandal0Subhabrata Mondal1Indian Statistical InstituteUniversity of CalcuttaIn this paper an analytic method is developed for solving Cauchy type singular integral equations of the first kind, over a finite interval. Chebyshev polynomials of the first kind, $T_n(x)$, second kind, $U_n(x)$, third kind, $V_n(x)$, and fourth kind, $W_n(x)$, corresponding to respective weight functions $W^{(1)}(x)=\frac{1}{\sqrt{1-x^2}},W^{(2)}(x)=\sqrt{1-x^2},W^{(3)}(x)=\sqrt{\frac{1+x}{1-x}},$ and $~ W^{(3)}(x)=\sqrt{\frac{1-x}{1+x}}, $ have been used to obtain the complete analytical solutions for four different cases.https://dergipark.org.tr/tr/download/article-file/677061singular integral equationcauchy kernelweight functionchebyshev polynomialsweight function |
| spellingShingle | B.n. Mandal Subhabrata Mondal Solution of Singular Integral Equations of the First Kind with Cauchy Kernel Communications in Advanced Mathematical Sciences singular integral equation cauchy kernel weight function chebyshev polynomials weight function |
| title | Solution of Singular Integral Equations of the First Kind with Cauchy Kernel |
| title_full | Solution of Singular Integral Equations of the First Kind with Cauchy Kernel |
| title_fullStr | Solution of Singular Integral Equations of the First Kind with Cauchy Kernel |
| title_full_unstemmed | Solution of Singular Integral Equations of the First Kind with Cauchy Kernel |
| title_short | Solution of Singular Integral Equations of the First Kind with Cauchy Kernel |
| title_sort | solution of singular integral equations of the first kind with cauchy kernel |
| topic | singular integral equation cauchy kernel weight function chebyshev polynomials weight function |
| url | https://dergipark.org.tr/tr/download/article-file/677061 |
| work_keys_str_mv | AT bnmandal solutionofsingularintegralequationsofthefirstkindwithcauchykernel AT subhabratamondal solutionofsingularintegralequationsofthefirstkindwithcauchykernel |