The a-points of Faber polynomials for a special function
Keyword(s):
Let f(ζ) be a power series of the formwhere lim sup |an|1/n < ∞. The Faber polynomials {fn(ζ)} (n = 0, 1, 2, …) are the polynomial parts of the formal expansion of (f(ζ))n about ζ = ∞. Series (1) defines an analytic element of an analytic function which we designate as w = f(ζ). Since at ζ = ∞ the analytic element is univalent in some neighborhood of infinity; thus the inverse of this element is uniquely determined in some neighborhood of w= ∞, and has a Laurent expansion of the formwhere lim sup |bn|1/n = p < ∞. Let ζ = g(w) be this single-valued function defined by (2) in |w| > p. No analytic continuation of g(w) will be considered.
1966 ◽
Vol 62
(4)
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pp. 637-642
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Keyword(s):
1981 ◽
Vol 33
(5)
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pp. 1255-1260
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Keyword(s):
1968 ◽
Vol 9
(2)
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pp. 146-151
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1959 ◽
Vol 55
(1)
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pp. 51-61
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1991 ◽
Vol 43
(1)
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pp. 182-212
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1982 ◽
Vol 34
(4)
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pp. 952-960
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