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Sonin worked on special functions, in particular cylindrical functions. He also worked on the Euler- Maclaurin summation formula.
Other topics Sonin studied included Bernoulli polynomials (Jacob Bernoulli) and approximate computation of definite integrals, continuing Chebyshev's work on numerical integration.
Together with A A Markov, Sonin prepared a two volume edition of Chebyshev's works in French and Russian.
References:
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