A RetroSearch Logo

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

Search Query:

Showing content from https://dlmf.nist.gov/4.9 below:

§4.9 Continued Fractions ‣ Logarithm, Exponential, Powers ‣ Chapter 4 Elementary Functions

§4.9 Continued Fractions Contents
  1. §4.9(i) Logarithms
  2. §4.9(ii) Exponentials
  3. §4.9(iii) Powers
§4.9(i) Logarithms

valid when z ∈ ℂ ∖ ( − ∞ , − 1 ] ∪ [ 1 , ∞ ) ; see Figure 4.23.1(i).

For other continued fractions involving logarithms see Lorentzen and Waadeland (1992, pp. 566–568). See also Cuyt et al. (2008, pp. 196–200).

§4.9(ii) Exponentials

For z ∈ ℂ ,

4.9.3 ez = 1 1 − z 1 + z 2 − z 3 + z 2 − z 5 + z 2 − ⁢ ⋯ = 1 + z 1 − z 2 + z 3 − z 2 + z 5 − z 2 + z 7 − ⁢ ⋯ = 1 + z 1 − ( z / 2 ) + z2 / ( 4 ⋅ 3 ) 1 + z2 / ( 4 ⋅ 15 ) 1 + z2 / ( 4 ⋅ 35 ) 1 + ⁢ ⋯ ⁢ z2 / ( 4 ⁢ ( 4 ⁢ n2 − 1 ) ) 1 + ⁢ ⋯

where

For other continued fractions involving the exponential function see Lorentzen and Waadeland (1992, pp. 563–564). See also Cuyt et al. (2008, pp. 193–195).

§4.9(iii) Powers

See Cuyt et al. (2008, pp. 217–220).

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