66[ ![ Aqua QA] ( https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg )] ( https://github.com/JuliaTesting/Aqua.jl )
77[ ![ JET QA] ( https://img.shields.io/badge/JET.jl-%E2%9C%88%EF%B8%8F-%23aa4444 )] ( https://github.com/aviatesk/JET.jl )
88
9- This package provides functions to compute the zeros of the J and Y functions,
10- and the zeros of their derivatives, where J and Y are Bessel functions of the first and second kind, respectively.
11-
12- For all functions described below, the order ` nu::Real ` is a finite number and ` n::Integer ` is a positive integer.
13- When ` nu isa AbstractFloat ` , the returned value has the same type as ` nu ` . When ` nu isa Integer ` , the usual
14- promotion rules apply, so that for most builtin integer types the output type will be ` Float64 ` . However,
15- when ` nu isa BigInt ` the output type will be ` BigFloat ` .
16-
17- When the output type is ` Float64 ` , the exported functions (` besselj_zero ` ,
18- ` bessely_zero ` , ` besselj_deriv_zero ` , and ` bessely_deriv_zero ` ) will use lookup tables to rapidly
19- return function zeros if the order ` nu ` is one of the first few values of ` 0, 1, ... ` and the enumerator
20- ` n ` is one of the first values of ` 1, 2, 3, ... ` . See the individual function docstrings for the actual
9+ This package provides functions to compute the zeros of the J and Y functions, and the zeros of
10+ their derivatives, where J and Y are Bessel functions of the first and second kind, respectively.
11+
12+ For all functions described below, the order ` nu::Real ` is a finite number and ` n::Integer ` is a
13+ positive integer. When ` nu isa AbstractFloat ` , the returned value has the same type as ` nu ` . When
14+ ` nu isa Integer ` , the usual promotion rules apply, so that for most builtin integer types the output
15+ type will be ` Float64 ` . However, when ` nu isa BigInt ` the output type will be ` BigFloat ` .
16+
17+ When the output type is ` Float64 ` , the exported functions (` besselj_zero ` , ` bessely_zero ` ,
18+ ` besselj_deriv_zero ` , and ` bessely_deriv_zero ` ) will use lookup tables to rapidly return function
19+ zeros if the order ` nu ` is one of the first few values of ` 0, 1, ... ` and the enumerator ` n ` is one
20+ of the first values of ` 1, 2, 3, ... ` . See the individual function docstrings for the actual
2121extents of the lookup tables.
2222
2323### Exported Functions
@@ -28,7 +28,7 @@ extents of the lookup tables.
2828besselj_zero (nu, n)
2929```
3030
31- Return the ` n ` th zero of the Bessel J function of order ` nu ` .
31+ Return the ` n ` th zero of the Bessel J function of order ` nu ` .
3232
3333#### bessely_zero(nu, n)
3434
@@ -44,8 +44,7 @@ Return the `n`th zero of the Bessel Y function of order `nu`.
4444besselj_deriv_zero (nu, n)
4545```
4646
47- Return the ` n ` th nonvanishing zero of the derivative of the Bessel J
48- function of order ` nu ` .
47+ Return the ` n ` th nonvanishing zero of the derivative of the Bessel J function of order ` nu ` .
4948
5049#### bessely_deriv_zero(nu, n)
5150
@@ -81,8 +80,7 @@ Asymptotic formula for the `n`th zero for the Bessel Y function of order `nu`.
8180FunctionZeros. besselj_deriv_zero_asymptotic (nu, n)
8281```
8382
84- Asymptotic formula for the ` n ` th nonvanishing zero of the derivative of the
85- Bessel J function of order ` nu ` .
83+ Asymptotic formula for the ` n ` th nonvanishing zero of the derivative of the Bessel J function of order ` nu ` .
8684
8785
8886#### FunctionZeros.bessely_deriv_zero_asymptotic(nu, n)
@@ -92,5 +90,3 @@ FunctionZeros.bessely_deriv_zero_asymptotic(nu, n)
9290```
9391
9492Asymptotic formula for the ` n ` th zero of the derivative of the Bessel Y function of order ` nu ` .
95-
96-
0 commit comments