BESSELY
Calculate Bessel function of the second kind for engineering problems involving wave propagation, heat transfer, and electromagnetic fields.
Excel
Google SheetsExcelGoogle Sheets=BESSELY(x, n)Quick Answer
Function BESSELY function calculates the Bessel function of the second kind (Yn(x)), also known as the Weber or Neumann function, used extensively in engineering and physics for problems involving cylindrical symmetry. With syntax =BESSELY(x, n) where x must be positive and n is the order (non-negative integer), it provides solutions to wave propagation, heat transfer, and electromagnetic field calculations. Unlike BESSELJ which is well-behaved at the origin, BESSELY has a logarithmic singularity at x=0, making it essential for boundary value problems in cylindrical geometries where specific physical constraints require this type of solution.
Practical Examples
Basic BESSELY Calculation (Order 0)
Calculate the Bessel Y function of order 0 for x=1.5
First Order Bessel Y Function
Calculate the Bessel Y function of order 1
Engineering Heat Transfer Calculation
Calculate temperature distribution in a cylindrical fin
Wave Propagation Analysis
Electromagnetic wave analysis in circular waveguides
Error Handling with IFERROR
Handle invalid inputs gracefully
Common Errors and Solutions
Invalid numeric value
The x argument is negative or zero, or n is non-integer. BESSELY has a singularity at x=0.
Ensure x is a positive number (x > 0) and n is a non-negative integer (0, 1, 2, etc.)
Validate input data before using BESSELY. Use data validation or conditional formatting to flag invalid inputs.
Wrong data type
One or both arguments are text values or cannot be converted to numbers
Check that both arguments are numeric values. Use VALUE() function to convert text to numbers if needed.
Use ISNUMBER() to validate inputs before applying BESSELY function.
Function not recognized
Excel version does not support BESSELY (requires Excel 2013 or later) or function name is misspelled
Verify Excel version is 2013 or later. Check spelling of function name. For older versions, use third-party add-ins or custom VBA functions.
Document minimum Excel version requirements for worksheets using engineering functions.
Advanced Tips and Best Practices
Understanding Function Behavior
Bessel functions of the second kind (Yn) oscillate like sine and cosine functions but with decreasing amplitude as x increases. They have a logarithmic singularity at x=0, approaching negative infinity, which distinguishes them from BESSELJ.
Computational Range
BESSELY works best for x values greater than 0.1. Very small x values (near 0) approach negative infinity and may cause numerical issues. For x near zero, consider if BESSELJ alone might satisfy your boundary conditions.
Order Selection
The order n must match your physical problem. Order 0 is most common for radially symmetric problems. Order 1 and higher appear when angular variation is present. For electromagnetic waveguides, different orders correspond to different propagation modes.
Combining with BESSELJ
Most real-world problems require linear combinations of BESSELJ and BESSELY to satisfy boundary conditions. The general solution is typically: Result = C1*BESSELJ(x,n) + C2*BESSELY(x,n), where C1 and C2 are determined by boundary conditions.
Error Handling for Production
Always wrap BESSELY in error handling for production spreadsheets: =IFERROR(BESSELY(x, n), "Check Parameters"). This prevents workflow interruption from invalid inputs and provides user-friendly feedback.
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Example Excel formula:
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