Excel BESSELY Function

What is BESSELY function in Excel?

The BESSELY function is one of the Engineering functions of Excel.

It Returns the Bessel function Yn(x).

We can find this function in Engineering category of the insert function Tab.

How to use BESSELY function in excel

1. Click on an empty cell (like F5 ).

2. Click on the fx icon (or press shift+F3).

3. In the insert function tab you will see all functions.

4. Select Engineering category.

5. Select BESSELY function.

6. Then select ok.

7. In the function arguments Tab you will see BESSELY function.

8. X section is the value at which to evaluate the function.

9. N section is the order of the Bessel function.

10. You will see the results in the formula result section.

Examples of BESSELY function in Excel

1. To calculate the value of Bessel function Y(2) at x = 5, use the following formula: =BESSELY(2,5)
2. To calculate the value of Bessel function Y(3) at x = 8, use the following formula: =BESSELY(3,8)
3. To calculate the value of Bessel function Y(0.5) at x = 4.5, use the following formula: =BESSELY(0.5,4.5)
4. To calculate the value of Bessel function Y(-2) at x = 3.2, use the following formula: =BESSELY(-2,3.2)
5. To calculate the value of Bessel function Y(4) at x = 7.5, use the following formula: =BESSELY(4,7.5)
6. To calculate the value of Bessel function Y(1.5) at x = 6.8, use the following formula: =BESSELY(1.5,6.8)
7. To calculate the value of Bessel function Y(0) at x = 2.5, use the following formula: =BESSELY(0,2.5)
8. To calculate the value of Bessel function Y(-3) at x = 9, use the following formula: =BESSELY(-3,9)
9. To calculate the value of Bessel function Y(2.5) at x = 4, use the following formula: =BESSELY(2.5,4)
10. To calculate the value of Bessel function Y(-0.5) at x = 5.7, use the following formula: =BESSELY(-0.5,5.7)

Example 1:

How to use BESSELY function in excel

You can see examples of BESSELY function below:

bessely(A2,B2) ----->>>>answer is  -87.14

bessely(A3,B3) ----->>>>answer is  -0.55

bessely(A4,B4) ----->>>>answer is  0.39

bessely(A5,B5) ----->>>>answer is  0.01

bessely(A6,B6) ----->>>>answer is  0.32

BESSELY Function in Excel: What You Need to Know

The BESSELY function in Excel is used to calculate the value of a Bessel function of the second kind for a given complex number. This function is useful in a variety of mathematical and scientific applications, particularly in the field of physics.

Understanding the Arguments of the BESSELY Function in Excel

The BESSELY function in Excel requires two arguments: x and n. The argument x is the complex number for which you want to calculate the Bessel function of the second kind, while the argument n specifies the order of the Bessel function.

For example, if you wanted to calculate the value of the Bessel function of the second kind for the complex number 3 + 4i with an order of 2, you would use the following formula:

=BESSELY(3+4i,2)

Step-by-Step Guide to Using the BESSELY Function in Excel

To use the BESSELY function in Excel, follow these steps:

1. Select the cell where you want the result to appear.
2. Type “=BESSELY(” into the formula bar.
3. Enter the complex number for which you want to calculate the Bessel function of the second kind, followed by a comma.
4. Enter the order of the Bessel function, followed by a closing parenthesis.
5. Press Enter.

For example, if you wanted to calculate the value of the Bessel function of the second kind for the complex number 3 + 4i with an order of 2, you would type the following formula in a cell:

=BESSELY(3+4i,2)

Syntax for the BESSELY Function in Excel: A Quick Reference

The syntax for the BESSELY function in Excel is as follows:

=BESSELY(x,n)

where x is the complex number for which you want to calculate the Bessel function of the second kind, and n specifies the order of the Bessel function.

For example, if you wanted to calculate the value of the Bessel function of the second kind for the complex number 3 + 4i with an order of 2, you would use the following formula:

=BESSELY(3+4i,2)

Complex Numbers and the BESSELY Function in Excel

The BESSELY function in Excel can be used to calculate the value of a Bessel function of the second kind for both real and complex numbers. However, when working with complex numbers, it is important to understand the properties of these numbers and how they affect the output of the BESSELY function.

For example, consider the complex number 3 + 4i. If we were to calculate the Bessel function of the second kind for this number with an order of 2, we would get a result of -0.019+0.545i. This result takes into account both the real and imaginary components of the input complex number.

Domain of the BESSELY Function: Explained

The domain of the BESSELY function in Excel is the set of all complex numbers. This means that the function can be used to calculate the Bessel function of the second kind for any complex number.

For example, if you wanted to calculate the value of the Bessel function of the second kind for the complex number -2 + 3i with an order of 1, you would use the following formula:

=BESSELY(-2+3i,1)

Range of the BESSELY Function in Excel: What You Should Know

The range of the BESSELY function in Excel is also a set of complex numbers. The exact range depends on the input values of x and n. However, in general, the range of the BESSELY function includes both real and imaginary numbers.

For example, if you wanted to calculate the value of the Bessel function of the second kind for the complex number 4 + 2i with an order of 3, you would use the following formula:

=BESSELY(4+2i,3)

This formula would return a complex number as the output.

Top Applications of the BESSELY Function in Excel

The BESSELY function in Excel has many applications in engineering, physics, and other fields. Some common applications include:

• Modeling electromagnetic waves
• Analyzing acoustic phenomena
• Solving heat transfer problems
• Calculating diffraction patterns

For example, if you were working on a project involving the propagation of sound through a medium, you could use the BESSELY function in Excel to model the behavior of the sound waves.

Accuracy of the BESSELY Function in Excel: How Reliable is It?

The accuracy of the BESSELY function in Excel depends on the complexity of the input values and the order of the Bessel function being calculated. In general, the function is accurate to within a few decimal places for most applications.

For example, if you were using the BESSELY function in Excel to calculate the diffraction pattern of light through a small aperture, you could expect the results to be accurate to within a few percent of the actual value.

Solving Differential Equations with the BESSELY Function in Excel

The BESSELY function in Excel can also be used to solve differential equations that involve Bessel functions of the second kind. This makes it a useful tool in many areas of science and engineering.

For example, consider the differential equation:

y” + 2xy’ + (x^2 – n^2)y = 0

where y(x) is the function we want to solve for, and n is the order of the Bessel function. If we use the BESSELY function in Excel to calculate the Bessel function of the second kind for a given value of n, we can use this value to solve the differential equation.

Limitations of the BESSELY Function in Excel: Factors to Consider

While the BESSELY function in Excel is a powerful tool for calculating Bessel functions of the second kind, there are some limitations and factors to consider when using this function. These include issues with numerical precision, convergence, and accuracy.

For example, if you were working on a project that required extremely high levels of numerical precision, you might need to use a more advanced tool than the BESSELY function in Excel.

BESSELY vs BESSELJ Function: Key Differences Explained

The BESSELY function in Excel is similar to the BESSELJ function, which calculates the Bessel function of the first kind. However, there are some key differences between these two functions based on the order of the Bessel function being calculated and the way the results are reported.

For example, if you were comparing the values of the Bessel function of the first and second kinds for a specific complex number and order, you would need to use both the BESSELJ and BESSELY functions in Excel.

Negative Values of x and the BESSELY Function in Excel

The BESSELY function in Excel can be used for negative values of x, but it may require additional steps or modifications to the formula depending on the order of the Bessel function being calculated.

For example, if you wanted to calculate the value of the Bessel function of the second kind for the complex number -3 + 4i with an order of 2, you would need to use the following modified formula:

=BESSELY(3-4i,2) + i*BESSELY(3+4i,2)

Plotting the BESSELY Function in Excel: A Guide

You can use Excel to plot the BESSELY function for specific values of x and n, which can help you visualize the behavior of this function for different inputs.

For example, if you wanted to plot the Bessel function of the second kind for the complex number 4 + 3i with an order of 1, you could follow these steps:

1. Create a new Excel spreadsheet.
2. Type the values of x and n in two adjacent cells (e.g., A1 and B1).
3. Enter the following formula into cell C1: =BESSELY(A1+B1*i,B1)
4. Copy this formula down the column to generate a range of values for the BESSELY function.
5. Select the range of values in column C and create a line chart to visualize the function.

Calculating the Hankel Function with the BESSELY Function in Excel

The Hankel function is a combination of the Bessel functions of the first and second kinds, and it can be calculated using the BESSELJ and BESSELY functions in Excel.

For example, if you wanted to calculate the value of the Hankel function for the complex number 2 + 3i with an order of 1, you would use the following formula:

=SQRT(PI/(2*(2+3i)))((BESSELJ(1,2+3i)+iBESSELY(1,2+3i)))

Converting Output of BESSELY Function to Degrees or Radians

The output of the BESSELY function in Excel is a complex number that represents the value of the Bessel function of the second kind for a given input. If you need to convert this output to degrees or radians, you can use the Excel functions DEGREES() or RADIANS(), respectively.

For example, if you wanted to calculate the value of the Bessel function of the second kind for the complex number 3 + 4i with an order of 2 and convert the result to degrees, you would use the following formula:

=DEGREES(BESSELY(3+4i,2))

Handling Large Values of x with the BESSELY Function in Excel

When working with very large values of x, the BESSELY function in Excel may return an error or produce inaccurate results. To handle large values of x, you can use alternative formulas or numerical methods to approximate the value of the Bessel function.

For example, if you needed to calculate the value of the Bessel function of the second kind for the complex number 1000 + 500i with an order of 10, you might use an approximation formula like the one found in Abramowitz and Stegun’s Handbook of Mathematical Functions.

Evaluating Multiple Values of x with the BESSELY Function in Excel

You can use Excel’s array formula feature to evaluate the BESSELY function for multiple values of x and n simultaneously. This can save time and improve efficiency when working with large data sets.

For example, if you had a list of complex numbers in column A and a corresponding list of orders in column B, you could use the following array formula in cell C1 to calculate the Bessel function of the second kind for all the input values:

{=BESSELY(A1:A10,B1:B10)}

Note that you must enter this formula as an array formula by pressing CTRL+SHIFT+ENTER instead of just ENTER.

Using BESSELY Function in Excel with Other Functions: Tips and Tricks

The BESSELY function in Excel can be combined with other functions to perform more complex calculations and analyses. For example, you might use the BESSELY function in conjunction with Excel’s IF() or AND() functions to conditionally calculate values based on certain criteria.

For example, if you had a list of complex numbers in column A and wanted to calculate the Bessel function of the second kind for each value only if it was greater than 0, you could use the following formula in cell B1:

=IF(A1>0,BESSELY(A1,2),””)

Speeding up Calculation of BESSELY Function in Excel: Best Practices

To improve the speed and efficiency of calculations involving the BESSELY function in Excel, it is important to follow best practices for spreadsheet design and optimization. This may include minimizing the use of volatile formulas, reducing the size of the data set, and using appropriate calculation options.

For example, if you were working with a large data set and experiencing slow performance when calculating the Bessel function of the second kind, you might consider using Excel’s manual calculation mode or optimizing your formula calculations to minimize the need for recalculation.

BESSELY related functions 

• BESSELI function
• BESSELK function
• BESSELJ function

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