BESSELJ function

PRO BASIC

The BESSELJ function in Jspreadsheet Formulas Pro is a mathematical tool that calculates the Bessel function of the first kind, J(x), for any given real or complex number x. This function is used in mathematical and engineering fields. You input a number, and the function processes it through the Bessel J equation, delivering the result. This is particularly useful for handling wave equations and heat conduction problems.

Documentation

Returns the value of the Bessel function of the first kind, J(x), for a specified point x and order n.

Syntax

BESSELJ(x, n)

Parameter	Description
`x`	The real or complex 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 BESSELJ function calculates the Bessel function, a solution to Bessel’s differential equation. The function takes two arguments: x (the value at which to evaluate the function), and n (the order of the Bessel function).

If x or n are non-numeric, BESSELJ will return a #VALUE! error.
If x or n are empty cells, BESSELJ will return a #VALUE! error.
If n is not an integer, BESSELJ will return a #NUM! error.
The function does not handle text or booleans, it only accepts numerical inputs.
If n is negative, BESSELJ will still calculate the function, since Bessel functions are defined for all real numbers.

Common Errors

Error	Description
#VALUE!	This error occurs when either `x` or `n` is non-numeric or an empty cell.
#NUM!	This error occurs when the `n` value is not an integer.

Best practices

Always make sure that both x and n are numerical values to avoid #VALUE! errors.

Ensure n is an integer, as BESSELJ does not work with non-integer orders and will return a #NUM! error.

BESSELJ can handle negative n values, but be aware that this could produce complex results. Make sure this is intended in your calculations.

Always check your result to verify it makes sense in the context of your data. Bessel functions can produce large outputs for large inputs, which can skew data if not handled properly.

Usage

A few examples using the BESSELJ function.

BESSELJ(5, 2)       // Returns the Bessel function value of order 2 at x = 5  
BESSELJ(-3.5, 4.2)  // Accepts a negative x and fractional n (if supported by engine)

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",
        "BESSELJ(x,n)"
    ],
    [
        1,
        0,
        "=BESSELJ(A2,B2)"
    ],
    [
        2,
        1,
        "=BESSELJ(A3,B3)"
    ],
    [
        3,
        2,
        "=BESSELJ(A4,B4)"
    ],
    [
        0.5,
        3,
        "=BESSELJ(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",
        "BESSELJ(x,n)"
    ],
    [
        1,
        0,
        "=BESSELJ(A2,B2)"
    ],
    [
        2,
        1,
        "=BESSELJ(A3,B3)"
    ],
    [
        3,
        2,
        "=BESSELJ(A4,B4)"
    ],
    [
        0.5,
        3,
        "=BESSELJ(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",
        "BESSELJ(x,n)"
    ],
    [
        1,
        0,
        "=BESSELJ(A2,B2)"
    ],
    [
        2,
        1,
        "=BESSELJ(A3,B3)"
    ],
    [
        3,
        2,
        "=BESSELJ(A4,B4)"
    ],
    [
        0.5,
        3,
        "=BESSELJ(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",
        "BESSELJ(x,n)"
    ],
    [
        1,
        0,
        "=BESSELJ(A2,B2)"
    ],
    [
        2,
        1,
        "=BESSELJ(A3,B3)"
    ],
    [
        3,
        2,
        "=BESSELJ(A4,B4)"
    ],
    [
        0.5,
        3,
        "=BESSELJ(A5,B5)"
    ]
]
            }]
        });
    }
}

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