Bessel functions of the first kind - Maple Help

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MTM[besseli], MTM[besselj] - Bessel functions of the first kind

MTM[besselk], MTM[bessely] - Bessel functions of the second kind

Calling Sequence

besseli(v,x)

besselj(v,x)

besselk(v,x)

bessely(v,x)

Parameters

v

-

algebraic expression (the order or index)

x

-

algebraic expression (the argument)

Description

• 

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

x22x2y+xxy+v2+x2y=0

• 

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

x22x2y+xxyv2+x2y=0

• 

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.  

Examples

withMTM:

xbesseljv,x

BesselJv+1,x+vBesselJv,xx

(1)

See Also

Bessel, MTM[diff], MTM[int], MTM[simplify]


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