Abel theorem

[′ä·bəl ′thir·əm] (mathematics) A theorem stating that if a power series in z converges for z = a, it converges absolutely for | z | < |="">a |. A theorem stating that if a power series in z converges to f (z) for | z | < 1="" and="" to="">a for z = 1, then the limit of f (z) as z approaches 1 equals a. A theorem stating that if the three series with n th term a_n, b_n, and c_n = a₀ b_n + a₁ b_n-1+ ⋯ + a_nb₀, respectively, converge, then the third series equals the product of the first two series.

单词	abel theorem
释义	Abel theorem Abel theorem [′ä·bəl ′thir·əm] (mathematics) A theorem stating that if a power series in z converges for z = a, it converges absolutely for \| z \| < \|="">a \|. A theorem stating that if a power series in z converges to f (z) for \| z \| < 1="" and="" to="">a for z = 1, then the limit of f (z) as z approaches 1 equals a. A theorem stating that if the three series with n th term a_n, b_n, and c_n = a₀ b_n + a₁ b_n-1+ ⋯ + a_nb₀, respectively, converge, then the third series equals the product of the first two series.
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