taylor e^{2z}

Lösung

taylor

e^{2 z}

1 + 2 z + 2 z^{2} + \frac{4}{3} z^{3} + \frac{2}{3} z^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d z} ( e ^{2 z} ) ( 0 )}{1 !} z + \frac{\frac{d ^{2}}{d z ^{2}} ( e ^{2 z} ) ( 0 )}{2 !} z^{2} + \frac{\frac{d ^{3}}{d z ^{3}} ( e ^{2 z} ) ( 0 )}{3 !} z^{3} + \dots

Evaluate Derivatives

= 1 + \frac{2}{1 !} z + \frac{4}{2 !} z^{2} + \frac{8}{3 !} z^{3} + \frac{16}{4 !} z^{4} + \dots

Fasse zusammen

= 1 + 2 z + 2 z^{2} + \frac{4}{3} z^{3} + \frac{2}{3} z^{4} + \dots

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