Bessel functions of the first kind
Bessel functions of the second kind
Bessel functions of the third kind
algebraic expression (the order or index)
algebraic expression (the argument)
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:
besselh are the Bessel functions of the third kind, also known as Hankel functions. They are linear combinations of the preceding Bessel functions:
Note that besselh(v,x) is a synonym for bessel(v,1,x) and besselh[k](v,x) is equivalent to besselh(v,k,x).
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.
The MTM[besseli], MTM[besselj], MTM[besselk], MTM[bessely] and MTM[besselh] commands were updated in Maple 2021.
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