Formule matematiche

Calcolo II

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Formula · Formule matematiche

15.5. Serie di Maclaurin fondamentali

Formula

Formula

sin x = n = 0 \sum \infty (- 1)^{n} \frac{x ^{2 n + 1}}{( 2 n + 1 )!} = x - \frac{x ^{3}}{3 !} + \frac{x ^{5}}{5 !} - \dots

Variabili

Correlata

Formula

e^{x} = n = 0 \sum \infty \frac{x ^{n}}{n !} = 1 + x + \frac{x ^{2}}{2 !} + \frac{x ^{3}}{3 !} + \dots

Correlata

Formula

cos x = n = 0 \sum \infty (- 1)^{n} \frac{x ^{2 n}}{( 2 n )!} = 1 - \frac{x ^{2}}{2 !} + \frac{x ^{4}}{4 !} - \dots

Correlata

Formula

\frac{1}{1 - x} = n = 0 \sum \infty x^{n}, ∣ x ∣ < 1

Correlata

Formula

ln (1 + x) = n = 1 \sum \infty (- 1)^{n - 1} \frac{x ^{n}}{n}, - 1 < x \leq 1

Correlata

Formula

arctan x = n = 0 \sum \infty (- 1)^{n} \frac{x ^{2 n + 1}}{2 n + 1}, ∣ x ∣ \leq 1