# BesselYZero

BesselYZero[n,k]

represents the k zero of the Bessel function of the second kind .

BesselYZero[n,k,x0]

represents the k zero greater than x0.

# Details

• Mathematical function, suitable for both symbolic and numerical manipulation.
• N[BesselYZero[n,k]] gives a numerical approximation so long as the specified zero exists.
• BesselYZero[n,k] represents the k zero greater than 0.
• BesselYZero can be evaluated to arbitrary numerical precision.
• BesselYZero automatically threads over lists.

# Examples

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## Basic Examples(5)

Evaluate numerically:

Evaluate symbolically:

Display zeros of the BesselY function over a subset of the reals:

Series expansion at the origin:

## Scope(17)

### Numerical Evaluation(6)

Evaluate numerically:

Find the first zero of greater than 50:

Evaluate to high precision:

Evaluate efficiently at high precision:

Evaluate at a noninteger second argument:

For BesselYZero[ν,k-α/π], the result is a zero of :

BesselYZero threads elementwise over lists:

### Specific Values(3)

Limiting value at infinity:

The first three zeros:

Find the first zero of BesselY[1,x] using Solve:

### Visualization(3)

Visualize the zeroes of BesselY as a step function:

Display zeros of the BesselY function:

Show the first zero greater than 4:

### Differentiation and Series Expansions(5)

Derivative of Bessel zero with respect to k:

Second derivative:

Find the Taylor expansion using Series:

Find the series expansion at Infinity:

Taylor expansion at a generic point:

## Properties & Relations(1)

Asymptotic behavior of BesselYZero[ν,k] for large k:

Wolfram Research (2007), BesselYZero, Wolfram Language function, https://reference.wolfram.com/language/ref/BesselYZero.html.

#### Text

Wolfram Research (2007), BesselYZero, Wolfram Language function, https://reference.wolfram.com/language/ref/BesselYZero.html.

#### CMS

Wolfram Language. 2007. "BesselYZero." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BesselYZero.html.

#### APA

Wolfram Language. (2007). BesselYZero. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BesselYZero.html

#### BibTeX

@misc{reference.wolfram_2024_besselyzero, author="Wolfram Research", title="{BesselYZero}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/BesselYZero.html}", note=[Accessed: 12-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_besselyzero, organization={Wolfram Research}, title={BesselYZero}, year={2007}, url={https://reference.wolfram.com/language/ref/BesselYZero.html}, note=[Accessed: 12-July-2024 ]}