besselj and bessely are the Bessel functions of the first and second kinds, respectively. They satisfy the Bessel equation:

besseli and besselk are the modified Bessel functions of the first and second kinds, respectively. They satisfy the modified Bessel equation:

By default, these functions will evaluate only when the result is an exact value, or when the input x is a floating point number.  When x is a symbolic expression, they will remain in function form so that they can be manipulated symbolically by themselves or as part of a larger expression.