The ClausenFunctions.jl package provides Julia implementations of the Standard Clausen functions and Glaisher-Clausen functions of integer order for real or complex arguments.
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)https://docs.juliahub.com/ClausenFunctions/
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].
ClausenFunctions.jl is licenced under the MIT License.