SOLUTION OF INTEGRAL EQUATIONS OF THE FIRST KIND WITH THE CONFLUENT HYPERDEOMETRIC FUNCTION AND NORMALIZED BESSEL FUNCTION IN THE KERNELS IN THE KLASS OF INTERGRABLE FUNCTIONS
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Abstract
Two integral equations of the first kind with the confluent hyperdeometric function and the normalized Bessel function in the kernels are considered. Y. Tamarkin obtained a well-known classical result on the solvability of the Abel integral equation in the space L1 (a,b) of integrable functions on a finite interval [a,b] of the real line. By Tamarkin’s method the solutions of the investigating equations in the closed form are obtained, and necessary and sufficient conditions for its solvability in the space of summable functions are given.
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References
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