Cyklometrická funkce: Porovnání verzí
Smazaný obsah Přidaný obsah
Řádek 185:
= \frac {\pi} {2}\,-\,\sum_{n=0}^\infty \frac {\binom{2n} n z^{2n+1}} {4^n (2n+1)}\,,\qquad\text{je-li }| z | \le 1\\[10pt]
\operatorname{arctg}z &= z - \frac {z^3} {3} +\frac {z^5} {5} -\frac {z^7} {7} +\dots\
= \sum_{n=0}^\infty \frac {(-1)^n z^{2n+1}} {2n+1}\,,\qquad\text{je-li }| z | \le 1,\ z \neq\pm\mathrm{i}\\[10pt]
\operatorname{arccotg}z &= \frac {\pi} {2} - \operatorname{arctg}z \ = \frac {\pi} {2}\,-\,\left( z - \frac {z^3} {3} +\frac {z^5} {5} -\frac {z^7} {7} +\dots\ \right)
= \frac {\pi} {2}\,-\,\sum_{n=0}^\infty \frac {(-1)^n z^{2n+1}} {2n+1}\,, \qquad \text{je-li }| z | \le 1,\ z \neq\pm\mathrm{i}\\[10pt]
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