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

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/

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].

Contributors

• @NAThompson: Implementation of the series acceleration for the real Clausen function cl2(::BigFloat) and cl(2,::BigFloat).

Copying

ClausenFunctions.jl is licenced under the MIT License.