Infinite Series Forms of Double Integrals
نویسندگان
چکیده
where 1 2 1 2 , , , r r θ θ are any real numbers, and n is any positive integer. We can obtain the infinite series forms of these double integrals using Taylor series expansions and integration term by term theorem; these are the major results of this paper (i.e., Theorems 1-3). Adams et al. [1], Nyblom [2], and Oster [3] provided some techniques to solve the integral problems. Yu [4-29], Yu and B. -H. Chen [30], Yu and Sheu [31], and T. -J. Chen and Yu [32,33,34] used complex power series method, integration term by term theorem, differentiation with respect to a parameter, Parseval’s theorem, area mean value theorem, and generalized Cauchy integral formula to solve some types of integral problems. In this paper, three examples are used to demonstrate the proposed calculations, and the manual calculations are verified using Maple.
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