TY  - JOUR
T1  - Solution of Singular Integral Equations of the First Kind with Cauchy Kernel
AU  - Mondal, Subhabrata
AU  - Mandal, B.n.
PY  - 2019
DA  - March
Y2  - 2019
DO  - 10.33434/cams.454740
JF  - Communications in Advanced Mathematical Sciences
PB  - Emrah Evren KARA
WT  - DergiPark
SN  - 2651-4001
SP  - 69
EP  - 74
VL  - 2
IS  - 1
LA  - en
AB  - 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.
KW  - Singular integral equation
KW  - Cauchy Kernel
KW  - Weight function
KW  - Chebyshev polynomials
KW  - Weight function
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UR  - https://doi.org/10.33434/cams.454740
L1  - https://dergipark.org.tr/en/download/article-file/677061
ER  -