BESSEL_JV

The cylindrical Bessel function of the first kind, J_v(z), is a solution to Bessel’s differential equation that remains finite at the origin for nonnegative integer order. It appears in wave, heat, and vibration problems with cylindrical symmetry.

This function evaluates J_v(z) for real order v and real argument z by calling SciPy’s implementation.

z^2 y'' + z y' + (z^2 - v^2)y = 0

where one regular solution is y = J_v(z).

Excel Usage

=BESSEL_JV(v, z)

v (float, required): Order of the Bessel function (dimensionless).
z (float, required): Argument where the function is evaluated (dimensionless).

Returns (float): Value of the Bessel function of the first kind at the specified order and argument.

Example 1: Order zero at unit argument

Inputs:

v	z
0	1

Excel formula:

=BESSEL_JV(0, 1)

Expected output:

0.765198

Example 2: First order at moderate argument

Inputs:

v	z
1	2.5

Excel formula:

=BESSEL_JV(1, 2.5)

Expected output:

0.497094

Example 3: Fractional order evaluation

Inputs:

v	z
0.5	3

Excel formula:

=BESSEL_JV(0.5, 3)

Expected output:

0.0650082

Example 4: Negative integer order

Inputs:

v	z
-1	2

Excel formula:

=BESSEL_JV(-1, 2)

Expected output:

-0.576725

Python Code

from scipy.special import jv as scipy_jv

def bessel_jv(v, z):
    """
    Compute the cylindrical Bessel function of the first kind for real order.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.jv.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        v (float): Order of the Bessel function (dimensionless).
        z (float): Argument where the function is evaluated (dimensionless).

    Returns:
        float: Value of the Bessel function of the first kind at the specified order and argument.
    """
    try:
        v = float(v)
        z = float(z)
        return float(scipy_jv(v, z))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

v *

Order of the Bessel function (dimensionless).

z *

Argument where the function is evaluated (dimensionless).