inc_gamma_imag {hawkesbow} | R Documentation |
Incomplete gamma function of imaginary argument
Description
Calculates the value of
Γ1(x,α)=∫x∞tα−1e−itdt
for 0<α<1
through the following relations:
∫0∞tα−1e−itdt=e−i2πα∫0∞tα−1e−tdt=e−i2παΓ(α).
obtained by contour integration, and:
∫0xtα−1e−itdt=∫0xtα−1cos(t)dt−i∫0xtα−1sin(t)dt=Ci(x,α)−iSi(x,α)
.
The first integral is calculated using function "tgamma" from the library
"boost::math", while the functions Ci and Si are approximated via
Taylor expansions.
Usage
inc_gamma_imag(x, alpha)
Arguments
x |
A non-negative number
|
alpha |
A number between 0 and 1 (strictly)
|
Value
The incomplete gamma function of imaginary argument (see Details)
Examples
inc_gamma_imag(1.0, 0.5)
[Package
hawkesbow version 1.0.3
Index]