The virtual code interface simplifies the gsl C language API by excluding the facilities for error estimates, omitting certain array valued functions, and subsuming sets of related functions within common ones where possible.
The functions with names in the following group take an argument of
the form (n,x), where n identifies the member of the
function family, and x is the argument to the function.
J
regular cylindrical Bessel functions
Y
irregular cylindrical Bessel functions
I
regular modified cylindrical Bessel functions
K
irregular modified cylindrical Bessel functions
For these functions, n can be either a natural number encoded
as in Representation of Numeric and Textual Data, or a floating
point number encoded as in math. The latter case specifies
functions of a fractional order. The relevant gsl function is called
based on the value and type of the parameter.
Two further related families of functions follow the same calling convention.
Isc
scaled regular modified cylindrical Bessel functions
Ksc
scaled irregular modified cylindrical Bessel functions
The foregoing functions are related to those above by an exponential scale factor as documented in the gsl reference manual.
Functions with names in the following group also take an argument of
the form (n,x), but are not defined for fractional orders and
so require a natural number for n.
j
regular spherical Bessel functions
y
irregular spherical Bessel functions
isc
regular modified spherical Bessel functions
ksc
irregular modified spherical Bessel functions
The functions in the remaining group follow idiosyncratic calling conventions.
zJ0, zJ1
These take a natural number n and return the nth root of
the regular cylindrical Bessel functions of order 0 or 1,
respectively.
zJnu
This takes a pair (nu,n) where nu is the (fractional)
order of a regular cylindrical Bessel function, n is a natural
number. It returns the nth zero of the function.
lnKnu
This takes a pair of floating point numbers (nu,x) where
nu is the (fractional) order of an irregular modified
cylindrical Bessel and x is the argument to the function,
and it returns the natural log of the function.