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.

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)"
    ]
]
            }]
        });
    }
}

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