Etheta_imaginary | R Documentation |
Calculates the value of
-ix e^{ix} E_\theta(ix) = -ix e{ix} \int_1^\infty t^{-\theta} e^{-ixt} \mathrm d t
for \theta > 0
.
This is achieved using recursive integrations by parts until 0 < \theta \le 1
,
then using either the exponential integral E1_imaginary
if \theta = 1
,
or the incomplete gamma function inc_gamma_imag
if 0 < \theta < 1
.
Etheta_imaginary(theta, x)
theta |
A strictly positive number |
x |
A vector of non-negative numbers |
The incomplete gamma function of imaginary argument with arbitrary power (see Details)
Etheta_imaginary(3.14, 1.0)
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