Transform - Numbers: Special

The Special template appears in the template list when a numeric field of type float32, float64, int8, int16, int32, int64uint8, uint16, uint32, or uint6, has been picked in the Transform pane.  The template computes Bessel functions, with specification of Order.

 

Special

Bessel function operations, with specification of Order. Order may be taken from a field, or specified by a value or by an expression.  Save the result into the specified Result destination using the specified numeric type.

 

  • Bessel 1st kind (jn) - The nth Bessel function of the first kind: Compute  the Bessel function Jn(x) for Order n using the source field number as x.  Specifying 2 for Order uses a J2(x) Bessel function.  Using 0 or 1 for the Order is equivalent to using J0(x) or J1(x), respectively. For example, specifying 2 for Order uses a J2(x) Bessel function.

 

 

  • Bessel 2nd kind (yn) - The nth Bessel function of the second kind: Compute the Bessel Function Yn(x) for Order n using the source field number as x.   For example, specifying 2 for Order uses a Y2(x) Bessel function.

 

 

Launch the template by choosing a numeric field and then double-clicking the Special template.   When the template launches we can specify options.

 

 

Special : Bessel 1st kind (jn)

The nth Bessel function of the first kind: Compute  the Bessel function Jn(x) for Order n using the source field number as x.  Specifying 2 for Order uses a J2(x) Bessel function.  Using 0 or 1 for the Order is equivalent to using J0(x) or J1(x), respectively.

 

We start with a table with a single Numbers field of type float64.   We have used the Layers pane to hide the mfd_id field, for a simpler illustration.

 

 

With the focus on the table window, in the Transform pane we choose the Numbers field and then the Special template.

 

 

In the Arithmetic template, we choose Bessel 1st kind (jn) as the Operation.    For the Order we enter 0.

 

For the Result destination, we choose New Field and then enter Bessel First as the name of the new field to add to the table.  We could use whatever name we want, but it is wise to use names that remind us of what they are supposed to be.   We leave the Result type at the default float64.

 

If we preferred, we could have chosen Same Field to write the result back to the Numbers field, updating it "in place," or we could have chosen some other existing numeric field in the table.

 

Press Transform.  

 

 

The template creates a new float64 type field called Bessel First and populates it with the value of the Bessel function J0(x)  (order of 0) for the value of Numbers in each record.

 

To get the Order 1 Bessel function results, we can re-run the transform.

 

 

For the Order we enter 1.

 

For the Result destination, from the pull down menu we choose the Bessel First field we created above.  

 

Press Transform.  

 

 

The template updates the existing Bessel First field with the value of the Bessel function J1(x) (order of 1) for the value of Numbers in each record.

 

To get the Order 2 Bessel function results, we can re-run the transform.

 

 

For the Order we enter 2.

 

For the Result destination, from the pull down menu we choose the Bessel First field we created above.  

 

Press Transform.  

 

 

The template updates the existing Bessel First field with the value of the Bessel function Jn(x) (n=2, for an order of 2) for the value of Numbers in each record.

 

Special : Bessel 2nd kind (yn)

The nth Bessel function of the second kind: Compute the Bessel Function Yn(x) for Order n using the source field number as x.  Specifying 2 for Order uses a Y2(x) Bessel function.  Using 0 or 1 for the Order is equivalent to using Y0(x) or Y1(x), respectively.

 

 

We start with a table with a single Numbers field of type float64.   We have used the Layers pane to hide the mfd_id field, for a simpler illustration.

 

 

With the focus on the table window, in the Transform pane we choose the Numbers field and then the Special template.

 

 

In the Arithmetic template, we choose Bessel 2nd kind (yn) as the Operation.    For the Order we enter 0.

 

For the Result destination, we choose New Field and then enter Bessel Second as the name of the new field to add to the table.  We could use whatever name we want, but it is wise to use names that remind us of what they are supposed to be.   We leave the Result type at the default float64.

 

If we preferred, we could have chosen Same Field to write the result back to the Numbers field, updating it "in place," or we could have chosen some other existing numeric field in the table.

 

Press Transform.  

 

 

The template creates a new float64 type field called Bessel Second and populates it with the value of the Bessel Function Y0(x) (order of 0) for the value of Numbers in each record.

 

To get the Order 1 Bessel function results, we can re-run the transform.

 

 

For the Order we enter 1.

 

For the Result destination, from the pull down menu we choose the Bessel Second  field we created above.  

 

Press Transform.  

 

 

The template updates the existing Bessel Second field with the value of the Bessel Function Y1(x) (order of 1) for the value of Numbers in each record.

 

To get the Order 2 Bessel function results, we can re-run the transform.

 

 

For the Order we enter 2.

 

For the Result destination, from the pull down menu we choose the Bessel Second field we created above.  

 

Press Transform.  

 

 

The template updates the existing Bessel Second field with the value of the Bessel Function Yn(x) (n=2, for an order of 2) for the value of Numbers in each record.

 

 

 

Notes

"Mathematics is the art of giving the same name to different things." - Henri Poincaré

 

See Also

Transform Pane

 

Transform Reference

 

Transform - Expression

 

Transform - Numeric Vectors

 

Transform - Numbers

 

Transform - Numbers: Arithmetic

 

Transform - Numbers: Bit Logic

 

Transform - Numbers: Copy

 

Transform - Numbers: Expression

 

Transform - Numbers: Hyperbolic

 

Transform - Numbers: Limit

 

Transform - Numbers: Round

 

Transform - Numbers: Trigonometric