BESSEL_YV

The cylindrical Bessel function of the second kind, Y_v(z), is the second linearly independent solution of Bessel’s differential equation. It is commonly used together with J_v(z) in cylindrical boundary-value and wave-radiation problems.

This function evaluates Y_v(z) for real order v and real argument z.

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

where one singular solution is y = Y_v(z).

Excel Usage

=BESSEL_YV(v, z)

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

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

Example 1: Zero order at unit argument

Inputs:

v	z
0	1

Excel formula:

=BESSEL_YV(0, 1)

Expected output:

0.088257

Example 2: First order at small positive argument

Inputs:

v	z
1	0.75

Excel formula:

=BESSEL_YV(1, 0.75)

Expected output:

-1.03759

Example 3: Fractional order evaluation

Inputs:

v	z
1.5	2

Excel formula:

=BESSEL_YV(1.5, 2)

Expected output:

-0.395623

Example 4: Second order at larger argument

Inputs:

v	z
2	5

Excel formula:

=BESSEL_YV(2, 5)

Expected output:

0.367663

Python Code

from scipy.special import yv as scipy_yv

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

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

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

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

    Returns:
        float: Value of the Bessel function of the second kind at the specified order and argument.
    """
    try:
        v = float(v)
        z = float(z)
        if z <= 0:
            return "Error: z must be greater than 0 for real-valued output"
        return float(scipy_yv(v, z))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

v *

Order of the Bessel function (dimensionless).

z *

Positive argument where the function is evaluated (dimensionless).