Table Of Contents

Spherical Bessel Function yn (G Dataflow)

Version:
    Last Modified: March 15, 2017

    Calculates the spherical Bessel function of the second kind.

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    x

    Input argument.

    This input accepts a double-precision, floating-point number or a complex double-precision, floating-point number.

    Default: The default value is 0 if x is a double-precision, floating-point number. The default value is 0 + 0i if x is a complex double-precision, floating-point number.

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    n

    Order of the spherical Bessel function.

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    error in

    Error conditions that occur before this node runs.

    The node responds to this input according to standard error behavior.

    Standard Error Behavior

    Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

    error in does not contain an error error in contains an error
    If no error occurred before the node runs, the node begins execution normally.

    If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

    If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

    Default: No error

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    yn(x)

    Value of the spherical Bessel function of the second kind.

    This output can return a double-precision, floating-point number or a complex double-precision, floating-point number.

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    error out

    Error information.

    The node produces this output according to standard error behavior.

    Standard Error Behavior

    Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

    error in does not contain an error error in contains an error
    If no error occurred before the node runs, the node begins execution normally.

    If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

    If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

    Algorithm for Calculating the Spherical Bessel Function of the Second Kind

    For the spherical Bessel function of the second kind of order n, yn(x) is a solution to the following differential equation.

    x 2 d 2 w d x 2 + 2 x d w d x + ( x 2 n ( n + 1 ) ) w = 0

    The following equation shows the relationship of the spherical Bessel function of the second kind to the Bessel function of the second kind.

    y n ( x ) = π 2 x Y v ( x ) , v = n + 1 2

    The function is defined according to the following intervals for the input values.

    n , x [ 0 , )

    This node supports the entire domain of this function that produces real-valued results. For any integer value of order n, the function is defined for nonnegative real values of x.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: This product does not support FPGA devices


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