List of Functions

Python Interface

Syntax	Return type	Symbol	User guide
`besselj(nu, z, n)`	`double`, `double complex`	\(\partial^n J_{\nu}(z) / \partial z^n\)	Bessel function of the first kind
`bessely(nu, z, n)`	`double`, `double complex`	\(\partial^n Y_{\nu}(z) / \partial z^n\)	Bessel function of the second kind (Weber function)
`besseli(nu, z, n)`	`double`, `double complex`	\(\partial^n I_{\nu}(z) / \partial z^n\)	Modified Bessel function of the first kind
`besselk(nu, z, n)`	`double`, `double complex`	\(\partial^n K_{\nu}(z) / \partial z^n\)	Modified Bessel function of the second kind
`besselh(nu, k, z, n)`	`double complex`	\(\partial^n H^{(k)}_{\nu}(z) / \partial z^n\)	Bessel function of the third kind (Hankel function)
`lngamma(x)`	`double`	\(\ln \Gamma(x)\)	Natural logarithm of Gamma function

Function Arguments:

Argument	Type	Symbol	Description
`nu`	`double`	\(\nu\)	Parameter of Bessel functions.
`k`	`int`	\(k\)	Can be `1` or `2` and sets the type of Hankel function.
`z`	`double`, `double complex`	\(z\)	Real or complex argument of the Bessel functions.
`x`	`double`	\(x\)	Real argument of the functions.
`n`	`int`	\(n\)	Order of derivative of function. Zero indicates no derivative.

Cython Interface

In Cython interface, the syntax of the real functions are similar to the Python interface. However, the syntax of complex functions start with the letter c in the beginning of each function as shown in the table below.

Symbol	Real Function	Complex Function
\(\partial^n J_{\nu}(z) / \partial z^n\)	`besselj(nu, x, n)`	`cbesselj(nu, z, n)`
\(\partial^n Y_{\nu}(z) / \partial z^n\)	`bessely(nu, x, n)`	`cbessely(nu, z, n)`
\(\partial^n I_{\nu}(z) / \partial z^n\)	`besseli(nu, x, n)`	`cbesseli(nu, z, n)`
\(\partial^n K_{\nu}(z) / \partial z^n\)	`besselk(nu, x, n)`	`cbesselk(nu, z, n)`
\(\partial^n H^{(k)}_{\nu}(z) / \partial z^n\)	`besselh(nu, k, x, n)`	`cbesselh(nu, k, z, n)`
\(\ln \Gamma(x)\)	`lngamma(x)`	N/A

In the above table:

x is of type double.
z is of type double complex.
Real functions return double type, with the exception of besselh that always returns double complex type.
Complex functions return double complex type.