Abel's Theorem - Remark

Remark

As an immediate consequence of this theorem, if z is any nonzero complex number for which the series \sum_{k=0}^\infty a_k z^k\! converges, then it follows that

in which the limit is taken from below.

Read more about this topic:  Abel's Theorem

Famous quotes containing the word remark:

    “I know not whether the remark is to our honour or otherwise, that lessons of wisdom have never such power over us, as when they are wrought into the heart, through the ground-work of a story which engages the passions: Is it that we are like iron, and must first be heated before we can be wrought upon?”
    —Laurence Sterne (1713–1768)

    “The Cretans are always liars, evil beasts, slow bellies.”
    —Bible: New Testament St. Paul, in Titus, 1:12.

    Cited by Paul, this remark is attributed to Epimenides.

    “The surest way to make a monkey of a man is to quote him. That remark in itself wouldn’t make any sense if quoted as it stands.”
    —Robert Benchley (1889–1945)