A RetroSearch Logo

Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Search Query:

Showing content from https://dlmf.nist.gov/4.38 below:

Further Properties ‣ Hyperbolic Functions ‣ Chapter 4 Elementary Functions

§4.38 Inverse Hyperbolic Functions: Further Properties Contents
  1. §4.38(i) Power Series
  2. §4.38(ii) Derivatives
  3. §4.38(iii) Addition Formulas
§4.38(i) Power Series

which requires z ( = x + i ⁢ y ) to lie between the two rectangular hyperbolas given by

§4.38(ii) Derivatives

In the following equations square roots have their principal values.

4.38.9 d d z ⁡ arcsinh ⁡ z = ( 1 + z2 ) − 1 / 2 . 4.38.10 d d z ⁡ arccosh ⁡ z = ± ( z2 − 1 ) − 1 / 2 , ℜ ⁡ z ≷ 0 . 4.38.11 d d z ⁡ arctanh ⁡ z = 1 1 − z2 . 4.38.12 d d z ⁡ arccsch ⁡ z = ∓ 1 z ⁢ ( 1 + z2 ) 1 / 2 , ℜ ⁡ z ≷ 0 . 4.38.13 d d z ⁡ arcsech ⁡ z = − 1 z ⁢ ( 1 − z2 ) 1 / 2 . 4.38.14 d d z ⁡ arccoth ⁡ z = 1 1 − z2 . §4.38(iii) Addition Formulas

The above equations are interpreted in the sense that every value of the left-hand side is a value of the right-hand side and vice-versa. All square roots have either possible value.

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.5