Etheta_imaginary: Incomplete gamma function of imaginary argument with...

In hawkesbow: Estimation of Hawkes Processes from Binned Observations

Description

Calculates the value of

-ix e^{ix} E_θ(ix) = -ix e{ix} \int_1^∞ t^{-θ} e^{-ixt} \mathrm d t

for θ > 0. This is achieved using recursive integrations by parts until 0 < θ ≤ 1, then using either the exponential integral E1_imaginary if θ = 1, or the incomplete gamma function inc_gamma_imag if 0 < θ < 1.

Usage

Etheta_imaginary(theta, x)

Arguments

theta	A strictly positive number
x	A vector of non-negative numbers

Value

The incomplete gamma function of imaginary argument with arbitrary power (see Details)

Examples

Etheta_imaginary(3.14, 1.0)

hawkesbow documentation built on April 10, 2021, 1:07 a.m.