BesselYZero

BesselYZero[n,k]

represents the k^(th) zero of the Bessel function of the second kind .

BesselYZero[n,k,x0]

represents the k^(th) 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^(th) 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:

TraditionalForm formatting:

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.

BibTeX

@misc{reference.wolfram_2021_besselyzero, author="Wolfram Research", title="{BesselYZero}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/BesselYZero.html}", note=[Accessed: 27-November-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_besselyzero, organization={Wolfram Research}, title={BesselYZero}, year={2007}, url={https://reference.wolfram.com/language/ref/BesselYZero.html}, note=[Accessed: 27-November-2021 ]}

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