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Rozvoj cyklometrických funkcí lze psát jako:
:<math>
\begin{align}
\arcsin z &= z \,+ \,\left( \frac {1} {2} \right) \frac {z^3} {3} \,
+ \,\left( \frac {1 \cdot 3} {2 \cdot 4} \right) \frac {z^5} {5} \,+ \,\left( \frac{1 \cdot 3 \cdot 5} {2 \cdot 4 \cdot 6 } \right) \frac{z^7} {7} \,+\, \cdotsdots\
= \sum_{n=0}^\infty \frac {\binom{2n} n z^{2n+1}} {4^n (2n+1)}; \,,\qquad \text{je-li }| z | \le 1 </math>\\[10pt]
:<math> \arccos z &= \frac {\pi} {2} \,- \,\arcsin z ▼
= z^\frac { -1\pi} {2}\,-\,\left( z + \left( \frac {1} {2} \right) \frac {z^ {-3 }} {3} + \left( \frac {1 \cdot 3} {2 \cdot 4 } \right) \frac {z^ {-5 }} {5} + \ cdotsdots\ \right) ▼▲:<math> \arccos z = \frac {\pi} {2} - \arcsin z
= \frac {\pi} {2} \,- \left( z + ,\left(sum_{n=0}^\infty \frac {1} \binom{22n} \right)n \frac {z^3{2n+1}} {3}4^n (2n+ 1)}\left( ,,\frac {1 qquad\cdot 3} text{2je-li \cdot 4}| \right) \frac {z^5} {5}| +\le 1\cdots\ \right) [10pt]
\operatorname{arctg}z &= z - \frac {\piz^3} {23} - \sum_{n=0}^\infty +\frac {\binom{2n} n z^{2n+1}5} {4^n (2n+1)5}; -\qquad |frac {z^7} |{7} +\dots\le 1 </math>
= \sum_{n=0}^\infty \frac { \binom{2n} (-1)^n z^{ -(2n+1 )}} { 4^n (2n+1 )} ; \,,\qquad \text{je-li}| z | \ gele 1 ,\ </math> z \neq\pm\mathrm{i}\\[10pt]▼
:<math>\operatorname{arccotg}z &= \arctanfrac {\pi} {2} - \operatorname{arctg}z \ = \frac {\pi} {2}\,-\,\left( z - \frac {z^3} {3} +\frac {z^5} {5} -\frac {z^7} {7} +\cdotsdots\ \right)
= \frac {\pi} {2}\,-\,\sum_{n=0}^\infty \frac {(-1)^n z^{2n+1}} {2n+1};\,, \qquad \text{je-li }| z | \le 1 ,\qquad z \neq \pm\mathrm{i,-i </math>}\\[10pt]
:<math> \arcsec z &= \arccos {(1/z)} ▼
:<math> \arccot z = \frac {\pi} {2} \,- \arctan,\left( z^{-1} + \ =left( \frac {\pi1} {2} - \left( z -right) \frac {z^{-3}} {3} + \left( \frac {z^51 \cdot 3} {52 \cdot 4} -\right) \frac {z^7{-5}} {75} + \cdotsdots\ \right)
= \frac {\pi} {2} \,- \,\sum_{n=0}^\infty \frac {(-1)^\binom{2n} n z^{-(2n+1)}} {4^n (2n+1)};\,, \qquad\text{je-li } | z | \lege 1 \qquad z \neq i,-i </math>[10pt]
:<math> \arccsc z &= \arcsin {(1/z)} ▼
= z^{-1}\,+\,\left( \frac {1} {2} \right) \frac {z^{-3}} {3}\,+\,\left( \frac {1 \cdot 3} {2 \cdot 4 } \right) \frac {z^{-5}} {5}\,+\,\dots\
▲:<math> \arcsec z = \arccos {(1/z)}
= \frac sum_{\pin=0} {2} - \left( z^{-1} + \left(infty \frac {1} \binom{22n} \right)n \frac {z^{-3(2n+1)}} {3}4^n (2n+ \left( \frac {1 \cdot 3)} {2 \cdot 4} ,,\right) qquad\frac {z^text{je-5}}li {5}| +z \cdots\| \right) ge 1
\end{align}
= \frac {\pi} {2} - \sum_{n=0}^\infty \frac {\binom{2n} n z^{-(2n+1)}} {4^n (2n+1)}; \qquad | z | \ge 1 </math>
</math>
▲:<math> \arccsc z = \arcsin {(1/z)}
▲= z^{-1} + \left( \frac {1} {2} \right) \frac {z^{-3}} {3} + \left( \frac {1 \cdot 3} {2 \cdot 4 } \right) \frac {z^{-5}} {5} +\cdots\
▲= \sum_{n=0}^\infty \frac {\binom{2n} n z^{-(2n+1)}} {4^n (2n+1)}; \qquad | z | \ge 1 </math>
== Literatura ==
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