Geodesic
Linear integro-differential equation with coefficients in the form of special sums
Problemy fiziki, matematiki i tehniki, no. 3 (2024), pp. 77-80

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A new linear hypersingular integro-differential equation of the first order has been explicitly solved. The equation is given on a closed curve located on the complex plane. The coefficients of the equation are expressed as sums of some summands. A finite number of the same functions are included in all summands of sums in a certain way. Classical and generalized Sokhotsky formulas, the theory of the Riemann boundary value problem, formulas for solving linear differential equations, properties of analytical functions are used. The solution is illustrated with an example.
Keywords: integro-differential equation, Sokhotsky formulas, Riemann boundary problem, linear differential equation. 
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     author = {A. P. Shilin},
     title = {Linear integro-differential equation with coefficients in the form of special sums},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {77--80},
     publisher = {mathdoc},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2024_3_a12/}
}
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A. P. Shilin. Linear integro-differential equation with coefficients in the form of special sums. Problemy fiziki, matematiki i tehniki, no. 3 (2024), pp. 77-80. http://geodesic.mathdoc.fr/item/PFMT_2024_3_a12/