Power Series Expansion for Hyperbolic Tangent Function/Also presented as
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Power Series Expansion for Hyperbolic Tangent Function: Also presented as
The Power Series Expansion for Hyperbolic Tangent Function can also be presented in the form:
| \(\ds \tanh x\) | \(=\) | \(\ds \sum_{n \mathop = 1}^\infty \frac {\paren {-1}^{n - 1} 2^{2 n} \paren {2^{2 n} - 1} {B_n}^* x^{2 n - 1} } {\paren {2 n}!}\) |
where ${B_n}^*$ denotes the archaic form of the Bernoulli numbers.
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 20$: Series for Hyperbolic Functions: $20.35$
- 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 22$: Taylor Series: Series for Hyperbolic Functions: $22.35.$