Category:Power Series Expansion for Real Area Hyperbolic Cosine

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This category contains pages concerning Power Series Expansion for Real Area Hyperbolic Cosine:


The (real) area hyperbolic cosine function has a Taylor series expansion:

\(\ds \arcosh x\) \(=\) \(\ds \map \ln {2 x} - \paren {\sum_{n \mathop = 1}^\infty \frac {\paren {2 n}!} {2^{2 n} \paren {n!}^2 \paren {2 n} x^{2 n} } }\)
\(\ds \) \(=\) \(\ds \map \ln {2 x} - \paren {\dfrac 1 {2 \times 2 x^2} + \dfrac {1 \times 3} {2 \times 4 \times 4 x^4} + \dfrac {1 \times 3 \times 5} {2 \times 4 \times 6 \times 6 x^6} + \cdots}\)

for $x \ge 1$.