See power series on Wiktionary
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"ref": "1983, Ian Stewart, David Tall, Complex Analysis, Cambridge University Press, page 259:",
"text": "Thus no single choice of z₀ will give a power series expansion of f(z) valid for all #x5C;textstylez#x5C;in#x5C;mathbb#x7B;C#x7D;#x5C;setminus#x5C;left#x5C;#x7B;-1,1#x5C;right#x5C;#x7D; even though f is analytic on this set.",
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"ref": "1988, Richard Courant, translated by E. J. McShane, Differential and Integral Calculus, 2nd edition, volume 1, Wiley, page 413:",
"text": "In this we may use as our starting-point a general discussion of the theory of power series with complex variables and complex coefficients. The construction of such a theory of power series offers no difficulty once we define the concept of limit in the domain of complex numbers; in fact, it follows the theory of real power series almost exactly.",
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"text": "1899, Oskar Bolza, The Theory of Functions, 2013, Reprint, Books on Demand, page 69,\nFrom this theorem (for which in many cases Cauchy's theorem on double sums may be substituted) follow easily the rules for the multiplication and division of power series, Taylor's theorem for power series along with the rules for differentiation of power series and series of power series."
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"Any infinite series of the general form ∑ᵢ₌₀ ᪲a_i(x-c)ⁱ."
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Download raw JSONL data for power series meaning in All languages combined (3.1kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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