let-f-z-n-0-a-n-z-n-a-0-1-a-1-3-and-n-2-a-n-3a-n-1-2-a-n-2-find-f-z-for-z-lt-1-z-C-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 30550 by abdo imad last updated on 23/Feb/18

let f(z)= Σ_(n≥0) a_n z^n /a_0 =1 ,a_1 =3 and ∀n≥2 a_n =3a_(n−1) −2 a_(n−2) find f(z) for ∣z∣<1 (z∈C) .

$${let}\:{f}\left({z}\right)=\:\sum_{{n}\geqslant\mathrm{0}} {a}_{{n}} {z}^{{n}} \:\:\:/{a}_{\mathrm{0}} =\mathrm{1}\:,{a}_{\mathrm{1}} =\mathrm{3}\:{and}\:\forall{n}\geqslant\mathrm{2} \\ $$$${a}_{{n}} =\mathrm{3}{a}_{{n}−\mathrm{1}} −\mathrm{2}\:{a}_{{n}−\mathrm{2}} \:\:\:\:{find}\:{f}\left({z}\right)\:{for}\:\mid{z}\mid<\mathrm{1}\:\:\left({z}\in{C}\right)\:. \\ $$

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let-f-z-n-0-a-n-z-n-a-0-1-a-1-3-and-n-2-a-n-3a-n-1-2-a-n-2-find-f-z-for-z-lt-1-z-C-

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