IT++ 4.3.1
|
Functions | |
double | itpp::besselj (int nu, double x) |
Bessel function of first kind of order nu for nu integer. | |
vec | itpp::besselj (int nu, const vec &x) |
Bessel function of first kind of order nu for nu integer. | |
double | itpp::besselj (double nu, double x) |
Bessel function of first kind of order nu. nu is real. | |
vec | itpp::besselj (double nu, const vec &x) |
Bessel function of first kind of order nu. nu is real. | |
double | itpp::bessely (int nu, double x) |
Bessel function of second kind of order nu. nu is integer. | |
vec | itpp::bessely (int nu, const vec &x) |
Bessel function of second kind of order nu. nu is integer. | |
double | itpp::bessely (double nu, double x) |
Bessel function of second kind of order nu. nu is real. | |
vec | itpp::bessely (double nu, const vec &x) |
Bessel function of second kind of order nu. nu is real. | |
double | itpp::besseli (double nu, double x) |
Modified Bessel function of first kind of order nu. nu is double. x is double. | |
vec | itpp::besseli (double nu, const vec &x) |
Modified Bessel function of first kind of order nu. nu is double. x is double. | |
double | itpp::besselk (int nu, double x) |
Modified Bessel function of second kind of order nu. nu is double. x is double. | |
vec | itpp::besselk (int nu, const vec &x) |
Modified Bessel function of second kind of order nu. nu is double. x is double. | |
end of math group
ITPP_EXPORT double itpp::besselj | ( | int | nu, |
double | x ) |
Bessel function of first kind of order nu for nu integer.
The bessel function of first kind is defined as:
\[J_{\nu}(x) = \sum_{k=0}^{\infty} \frac{ (-1)^{k} }{k! \Gamma(\nu+k+1) } \left(\frac{x}{2}\right)^{\nu+2k} \]
where \(\nu\) is the order and \( 0 < x < \infty \).
Definition at line 44 of file bessel.cpp.
Referenced by itpp::FIR_Fading_Generator::Jakes_filter().
ITPP_EXPORT vec itpp::besselj | ( | int | nu, |
const vec & | x ) |
Bessel function of first kind of order nu for nu integer.
Definition at line 46 of file bessel.cpp.
ITPP_EXPORT double itpp::besselj | ( | double | nu, |
double | x ) |
Bessel function of first kind of order nu. nu is real.
Definition at line 56 of file bessel.cpp.
ITPP_EXPORT vec itpp::besselj | ( | double | nu, |
const vec & | x ) |
Bessel function of first kind of order nu. nu is real.
Definition at line 58 of file bessel.cpp.
ITPP_EXPORT double itpp::bessely | ( | int | nu, |
double | x ) |
Bessel function of second kind of order nu. nu is integer.
The Bessel function of second kind is defined as:
\[Y_{\nu}(x) = \frac{J_{\nu}(x) \cos(\nu\pi) - J_{-\nu}(x)}{\sin(\nu\pi)} \]
where \(\nu\) is the order and \( 0 < x < \infty \).
Definition at line 68 of file bessel.cpp.
ITPP_EXPORT vec itpp::bessely | ( | int | nu, |
const vec & | x ) |
Bessel function of second kind of order nu. nu is integer.
Definition at line 70 of file bessel.cpp.
ITPP_EXPORT double itpp::bessely | ( | double | nu, |
double | x ) |
Bessel function of second kind of order nu. nu is real.
Definition at line 79 of file bessel.cpp.
ITPP_EXPORT vec itpp::bessely | ( | double | nu, |
const vec & | x ) |
Bessel function of second kind of order nu. nu is real.
Definition at line 81 of file bessel.cpp.
ITPP_EXPORT double itpp::besseli | ( | double | nu, |
double | x ) |
Modified Bessel function of first kind of order nu. nu is double. x is double.
The Modified Bessel function of first kind is defined as:
\[I_{\nu}(x) = i^{-\nu} J_{\nu}(ix) \]
where \(\nu\) is the order and \( 0 < x < \infty \).
Definition at line 91 of file bessel.cpp.
ITPP_EXPORT vec itpp::besseli | ( | double | nu, |
const vec & | x ) |
Modified Bessel function of first kind of order nu. nu is double. x is double.
Definition at line 93 of file bessel.cpp.
ITPP_EXPORT double itpp::besselk | ( | int | nu, |
double | x ) |
Modified Bessel function of second kind of order nu. nu is double. x is double.
The Modified Bessel function of second kind is defined as:
\[K_{\nu}(x) = \frac{\pi}{2} i^{\nu+1} [J_{\nu}(ix) + i Y_{\nu}(ix)] \]
where \(\nu\) is the order and \( 0 < x < \infty \).
Definition at line 103 of file bessel.cpp.
ITPP_EXPORT vec itpp::besselk | ( | int | nu, |
const vec & | x ) |
Modified Bessel function of second kind of order nu. nu is double. x is double.
Definition at line 105 of file bessel.cpp.