BESSELY function
PRO
BASIC
The BESSELY
function in Jspreadsheet Formulas Pro calculates the Bessel function of the second kind, denoted as Y(x)
. This function is widely used in engineering, physics, and signal processing, particularly in contexts involving cylindrical or spherical symmetry such as vibrations or acoustic wave equations.
It accepts a positive real number x
and a function order n
, returning the corresponding Yₙ(x)
value.
Documentation
Returns the Bessel function of the second kind, Y(x), for a given positive real number x.
Category
Engineering
Syntax
BESSELY(x, n)
Parameter | Description |
---|---|
x |
The positive real number for which to calculate the Bessel function. |
n |
The order of the Bessel function. Must be a nonnegative integer or a real number greater than -1. |
Behavior
The 'BESSELY' function is used to calculate the Bessel function Yₙ(x)
. This function requires two arguments: the order of the function 'n' and the value 'x' for which the function is computed. Here's how it handles various inputs:
- Numeric Values: Both the inputs 'n' and 'x' should be numbers for the function to work correctly.
- Empty Cells: If any of the inputs are empty cells, the function will return a '#NUM!' error.
- Text Values: If the inputs are text instead of numbers, the function will return a '#VALUE!' error.
- Booleans Values: If boolean values (TRUE or FALSE) are input, they will be coerced to numeric values, with TRUE being interpreted as 1 and FALSE as 0.
- Negative x: Triggers a #NUM! error, as Y(x) is undefined for negative real x.
- Decimal n: Supported if greater than -1; may be truncated based on environment.
Common Errors
Error | Description |
---|---|
#NUM! | This error occurs when the 'x' value is less than zero, or if any of the inputs are empty cells. |
#VALUE! | This error is returned when any of the inputs are non-numeric, such as text. |
Best practices
- Always ensure that both arguments are numeric. The 'BESSELY' function does not work with text inputs.
- Be cautious when using cell references or other functions as inputs. Make sure they will return numeric values to prevent errors.
- The 'x' value should be greater than or equal to zero. Negative values will result in a '#NUM!' error.
- Use error checking functions like 'IFERROR' to handle possible errors and make your spreadsheet more robust.
Usage
A few examples using the BESSELY function.
BESSELY(5, 2) // Returns ≈ 0.367662879
BESSELY(1.5, 0) // Returns ≈ 0.382448925
BESSELY(3, 4.2) // Returns ≈ -0.916682846
Interactive Spreadsheet Demo
<html>
<script src="https://jspreadsheet.com/v11/jspreadsheet.js"></script>
<script src="https://jsuites.net/v5/jsuites.js"></script>
<link rel="stylesheet" href="https://jsuites.net/v5/jsuites.css" type="text/css" />
<link rel="stylesheet" href="https://jspreadsheet.com/v11/jspreadsheet.css" type="text/css" />
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Material+Icons" />
<script src="https://cdn.jsdelivr.net/npm/@jspreadsheet/formula-pro/dist/index.min.js"></script>
<div id="spreadsheet"></div>
<script>
// Set your JSS license key (The following key only works for one day)
jspreadsheet.setLicense('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');
// Set the extensions
jspreadsheet.setExtensions({ formula });
// Create a new spreadsheet
jspreadsheet(document.getElementById('spreadsheet'), {
worksheets: [{
data: [
[
"x",
"n",
"BESSELY Result"
],
[
2.5,
1,
"=BESSELY(A2,B2)"
],
[
4.0,
0,
"=BESSELY(A3,B3)"
],
[
1.8,
2,
"=BESSELY(A4,B4)"
],
[
6.2,
3,
"=BESSELY(A5,B5)"
]
]
}]
});
</script>
</html>
import React, { useRef } from "react";
import { Spreadsheet, Worksheet, jspreadsheet } from "@jspreadsheet/react";
import formula from "@jspreadsheet/formula-pro";
import "jsuites/dist/jsuites.css";
import "jspreadsheet/dist/jspreadsheet.css";
// Set license
jspreadsheet.setLicense('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');
// Set the extensions
jspreadsheet.setExtensions({ formula });
export default function App() {
// Spreadsheet array of worksheets
const spreadsheet = useRef();
// Worksheet data
const data = [
[
"x",
"n",
"BESSELY Result"
],
[
2.5,
1,
"=BESSELY(A2,B2)"
],
[
4.0,
0,
"=BESSELY(A3,B3)"
],
[
1.8,
2,
"=BESSELY(A4,B4)"
],
[
6.2,
3,
"=BESSELY(A5,B5)"
]
];
// Render component
return (
<Spreadsheet ref={spreadsheet}>
<Worksheet data={data} />
</Spreadsheet>
);
}
<template>
<Spreadsheet ref="spreadsheet">
<Worksheet :data="data" />
</Spreadsheet>
</template>
<script>
import { Spreadsheet, Worksheet, jspreadsheet } from "@jspreadsheet/vue";
import "jsuites/dist/jsuites.css";
import "jspreadsheet/dist/jspreadsheet.css";
import formula from "@jspreadsheet/formula-pro";
// Set license
jspreadsheet.setLicense('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');
// Set the extensions
jspreadsheet.setExtensions({ formula });
export default {
components: {
Spreadsheet,
Worksheet,
},
data() {
// Worksheet data
const data = [
[
"x",
"n",
"BESSELY Result"
],
[
2.5,
1,
"=BESSELY(A2,B2)"
],
[
4.0,
0,
"=BESSELY(A3,B3)"
],
[
1.8,
2,
"=BESSELY(A4,B4)"
],
[
6.2,
3,
"=BESSELY(A5,B5)"
]
]
return {
data
};
}
}
</script>
import { Component, ViewChild, ElementRef } from "@angular/core";
import jspreadsheet from "jspreadsheet";
import * as formula from "@jspreadsheet/formula-pro";
// Set your JSS license key (The following key only works for one day)
jspreadsheet.setLicense('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');
// Set the extensions
jspreadsheet.setExtensions({ formula });
@Component({
standalone: true,
selector: "app-root",
template: `<div #spreadsheet></div>`
})
export class AppComponent {
@ViewChild("spreadsheet") spreadsheet: ElementRef;
// Worksheets
worksheets: jspreadsheet.worksheetInstance[];
// Create a new data grid
ngAfterViewInit() {
// Create spreadsheet
this.worksheets = jspreadsheet(this.spreadsheet.nativeElement, {
worksheets: [{
data: [
[
"x",
"n",
"BESSELY Result"
],
[
2.5,
1,
"=BESSELY(A2,B2)"
],
[
4.0,
0,
"=BESSELY(A3,B3)"
],
[
1.8,
2,
"=BESSELY(A4,B4)"
],
[
6.2,
3,
"=BESSELY(A5,B5)"
]
]
}]
});
}
}