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 an, bn, and cn = a0 bn + a1 bn-1+ ⋯ + anb0, respectively, converge, then the third series equals the product of the first two series.
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