DebyeFunctions

Implements some Debye functions, defined as:

{D_n\left(x\right)} = {{\frac{n}{x^n}} \cdot {\int_0^x {{\frac{t^n}{e^t - 1}} dt}}}

Currently the only tested values of n are integers from one to four.

Usage examples

Float64

The Evaluate submodule currently contains Float64-specific functionality. Use DebyeFunctions.Evaluate.evaluate(x, Val(n)) to calculate D_n(x), where x is a Float64 value.

julia> import DebyeFunctions

julia> DebyeFunctions.Evaluate.evaluate(-1.3, Val(3))
1.5703513708666639

julia> DebyeFunctions.Evaluate.evaluate(0.0, Val(3))
1.0

julia> DebyeFunctions.Evaluate.evaluate(9.0, Val(3))
0.026199892587964884

Generic

The DebyeQuadrature submodule contains an implementation of the Debye functions that can support any floating-point number type.

julia> import DebyeFunctions

julia> relative_tolerance = 2.0^-200
6.223015277861142e-61

julia> quadrature_order = 20
20

julia> DebyeFunctions.DebyeQuadrature.evaluate(big"-1.3", Val(3), relative_tolerance, quadrature_order)
1.570351370866663802241585778821552067132056646808002008054568886589056000865476