https://github.com/expander/clausenfunctions.jl
Clausen functions in Julia
https://github.com/expander/clausenfunctions.jl
julia math special-functions
Last synced: 6 months ago
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Clausen functions in Julia
- Host: GitHub
- URL: https://github.com/expander/clausenfunctions.jl
- Owner: Expander
- License: mit
- Created: 2021-09-19T17:31:10.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2024-12-19T19:08:39.000Z (over 1 year ago)
- Last Synced: 2025-02-01T09:11:14.323Z (about 1 year ago)
- Topics: julia, math, special-functions
- Language: Julia
- Homepage:
- Size: 563 KB
- Stars: 5
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
- Citation: CITATION.cff
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README
ClausenFunctions.jl
===================
[](https://github.com/Expander/ClausenFunctions.jl/actions/workflows/build.yml)
[](https://coveralls.io/github/Expander/ClausenFunctions.jl)
The ClausenFunctions.jl package provides Julia implementations of the
Standard Clausen functions and Glaisher-Clausen functions of integer
order for real or complex arguments.
Example
-------
```.jl
using ClausenFunctions
# real arguments
cl1(1.0) # Standard Clausen function Cl_1(x)
cl2(1.0) # Standard Clausen function Cl_2(x)
cl3(1.0) # Standard Clausen function Cl_3(x)
cl4(1.0) # Standard Clausen function Cl_4(x)
cl5(1.0) # Standard Clausen function Cl_5(x)
cl6(1.0) # Standard Clausen function Cl_6(x)
cl(10, 1.0) # Standard Clausen function Cl_n(x)
cl(10, big"1") # Standard Clausen function Cl_n(x)
sl(10, 1.0) # Glaisher-Clausen function Sl_n(x)
sl(10, big"1") # Glaisher-Clausen function Sl_n(x)
# complex arguments
cl1(1.0 + 1.0im) # Standard Clausen function Cl_1(x)
cl(10, 1.0 + 1.0im) # Standard Clausen function Cl_n(x)
cl(10, big"1" + 1im) # Standard Clausen function Cl_n(x)
sl(10, 1.0 + 1.0im) # Glaisher-Clausen function Sl_n(x)
sl(10, big"1" + 1im) # Glaisher-Clausen function Sl_n(x)
```
Documentation
-------------
[https://docs.juliahub.com/ClausenFunctions/](https://docs.juliahub.com/ClausenFunctions/)
Notes
-----
The implementation of the Standard Clausen function `cl(n,x)` for real
`x` follows the approach presented in [Jiming Wu, Xiaoping Zhang,
Dongjie Liu, "An efficient calculation of the Clausen functions
Cl_n(θ)(n >= 2)", Bit Numer Math 50, 193-206 (2010)
[https://doi.org/10.1007/s10543-009-0246-8](https://doi.org/10.1007/s10543-009-0246-8)].
Copying
-------
ClausenFunctions.jl is licenced under the MIT License.