Bessel

0th

Percentile

Bessel functions

Bessel functons as per the Gnu Scientific Library, reference manual section 7.5

Keywords
array
Usage
bessel_J0(x, give=FALSE, strict=TRUE)
bessel_J1(x, give=FALSE, strict=TRUE)
bessel_Jn(n,x, give=FALSE, strict=TRUE)
bessel_Jn_array(nmin,nmax,x, give=FALSE, strict=TRUE)
bessel_Y0(x, give=FALSE, strict=TRUE)
bessel_Y1(x, give=FALSE, strict=TRUE)
bessel_Yn(n,x, give=FALSE, strict=TRUE)
bessel_Yn_array(nmin, nmax, x, give=FALSE, strict=TRUE)
bessel_I0(x, give=FALSE, strict=TRUE)
bessel_I1(x, give=FALSE, strict=TRUE)
bessel_In(n, x, give=FALSE, strict=TRUE)
bessel_In_array(nmin, nmax, x, give=FALSE, strict=TRUE)
bessel_I0_scaled(x, give=FALSE, strict=TRUE)
bessel_I1_scaled(x, give=FALSE, strict=TRUE)
bessel_In_scaled(n, x, give=FALSE, strict=TRUE)
bessel_In_scaled_array(nmin, nmax, x, give=FALSE, strict=TRUE)
bessel_K0(x, give=FALSE, strict=TRUE)
bessel_K1(x, give=FALSE, strict=TRUE)
bessel_Kn(n, x, give=FALSE, strict=TRUE)
bessel_Kn_array(nmin, nmax, x, give=FALSE, strict=TRUE)
bessel_K0_scaled(x, give=FALSE, strict=TRUE)
bessel_K1_scaled(x, give=FALSE, strict=TRUE)
bessel_Kn_scaled(n, x, give=FALSE, strict=TRUE)
bessel_Kn_scaled_array(nmin, nmax, x, give=FALSE, strict=TRUE)
bessel_j0(x, give=FALSE, strict=TRUE)
bessel_j1(x, give=FALSE, strict=TRUE)
bessel_j2(x, give=FALSE, strict=TRUE)
bessel_jl(l,x, give=FALSE, strict=TRUE)
bessel_jl_array(lmax,x, give=FALSE, strict=TRUE)
bessel_jl_steed_array(lmax, x, give=FALSE, strict=TRUE)
bessel_y0(x, give=FALSE, strict=TRUE)
bessel_y1(x, give=FALSE, strict=TRUE)
bessel_y2(x, give=FALSE, strict=TRUE)
bessel_yl(l, x, give=FALSE, strict=TRUE)
bessel_yl_array(lmax, x, give=FALSE, strict=TRUE)
bessel_i0_scaled(x, give=FALSE, strict=TRUE)
bessel_i1_scaled(x, give=FALSE, strict=TRUE)
bessel_i2_scaled(x, give=FALSE, strict=TRUE)
bessel_il_scaled(l, x, give=FALSE, strict=TRUE)
bessel_il_scaled_array(lmax, x, give=FALSE, strict=TRUE)
bessel_k0_scaled(x, give=FALSE, strict=TRUE)
bessel_k1_scaled(x, give=FALSE, strict=TRUE)
bessel_k2_scaled(x, give=FALSE, strict=TRUE)
bessel_kl_scaled(l,x, give=FALSE, strict=TRUE)
bessel_kl_scaled_array(lmax,x, give=FALSE, strict=TRUE)
bessel_Jnu(nu, x, give=FALSE, strict=TRUE)
bessel_sequence_Jnu(nu, v, mode=0, give=FALSE, strict=TRUE)
bessel_Ynu(nu, x, give=FALSE, strict=TRUE)
bessel_Inu(nu, x, give=FALSE, strict=TRUE)
bessel_Inu_scaled(nu, x, give=FALSE, strict=TRUE)
bessel_Knu(nu, x, give=FALSE, strict=TRUE)
bessel_lnKnu(nu, x, give=FALSE, strict=TRUE)
bessel_Knu_scaled(nu, x, give=FALSE, strict=TRUE)
bessel_zero_J0(s, give=FALSE, strict=TRUE)
bessel_zero_J1(s, give=FALSE, strict=TRUE)
bessel_zero_Jnu(nu, s, give=FALSE, strict=TRUE)
Arguments
x
input: real valued
v
input: real valued
n
input: integer valued
nmin
input: integer valued
nmax
input: integer valued
lmax
input: integer valued
l
input: integer valued
s
input: integer valued
nu
input: real valued
mode
calc mode
give
give error
strict
strict or not
Details

All as for the GSL library, except for process.bessel.args(), which ensures that the arguments n and x are suitable for passing to the relevant C routine.

Aliases
  • Bessel
  • bessel_J0
  • bessel_J1
  • bessel_Jn
  • bessel_Jn_array
  • bessel_Y0
  • bessel_Y1
  • bessel_Yn
  • bessel_Yn_array
  • bessel_I0
  • bessel_I1
  • bessel_In
  • bessel_In_array
  • bessel_I0_scaled
  • bessel_I1_scaled
  • bessel_In_scaled
  • bessel_In_scaled_array
  • bessel_K0
  • bessel_K1
  • bessel_Kn
  • bessel_Kn_array
  • bessel_K0_scaled
  • bessel_K1_scaled
  • bessel_Kn_scaled
  • bessel_Kn_scaled_array
  • bessel_j0
  • bessel_j1
  • bessel_j2
  • bessel_jl
  • bessel_jl_array
  • bessel_jl_steed_array
  • bessel_y0
  • bessel_y1
  • bessel_y2
  • bessel_yl
  • bessel_yl_array
  • bessel_i0_scaled
  • bessel_i1_scaled
  • bessel_i2_scaled
  • bessel_il_scaled
  • bessel_il_scaled_array
  • bessel_k0_scaled
  • bessel_k1_scaled
  • bessel_k2_scaled
  • bessel_kl_scaled
  • bessel_kl_scaled_array
  • bessel_Jnu
  • bessel_sequence_Jnu
  • bessel_Ynu
  • bessel_Inu
  • bessel_Inu_scaled
  • bessel_Knu
  • bessel_lnKnu
  • bessel_Knu_scaled
  • bessel_zero_J0
  • bessel_zero_J1
  • bessel_zero_Jnu
Examples
x <- seq(from=0,to=15,len=100)
plot(x,bessel_J0(x),xlim=c(0,15),ylim=c(-0.8,1),type="l",xaxt="n",yaxt="n",bty="n",xlab="",ylab="",main="Figure 9.1, p359")
axis(1,pos=0)
axis(2,pos=0)
lines(x,bessel_Y0(x))
lines(x,bessel_J1(x),lty=2)
lines(x,bessel_Y1(x),lty=2)

x <- seq(from=0,to=13,len=100)
 matplot(x,t(bessel_jl_array(3,x)),col="black",type="l",xaxt="n",yaxt="n",bty="n",xlab="",ylab="",main="Figure 10.1, p438")
axis(1,pos=0)
axis(2,pos=0)


x <- seq(from=0 ,to=5,by=0.1)
cbind(x, bessel_J0(x),bessel_J1(x),bessel_Jn(2,x))      #table 9.1, p390
cbind(x, bessel_Y0(x),bessel_Y1(x),bessel_Yn(2,x))      #table 9.2, p391
t(bessel_Jn_array(3,9,x*2))                             #table 9.2, p398

cbind(                       x,                         #table 9.8, p416
        exp(-x)*bessel_I0  (x),
        exp(-x)*bessel_I1  (x),
         x^(-2)*bessel_In(2,x)
)

cbind(                      x,                          #table 9.8, p417
        exp(x)*bessel_K0  (x),
        exp(x)*bessel_K1  (x),
         x^(2)*bessel_Kn(2,x)
)

cbind(x,                                                #table 10.1 , p457
    bessel_j0(x),
    bessel_j1(x),
    bessel_j2(x),
    bessel_y0(x),
    bessel_y1(x),
    bessel_y2(x)
)


bessel_Jnu(0.5,1.123)
bessel_Ynu(0.5,1.123)
bessel_Inu(0.5,1.123)
bessel_Inu_scaled(0.5,1.123)

bessel_Knu(0.5,1.123)
bessel_lnKnu(0.5,1.123)
bessel_Knu_scaled(0.5,1.123)

x <- 1:20
cbind(x,bessel_zero_J0(x), bessel_zero_J1(x), bessel_zero_Jnu(n=3,x))
#Table 9.5, p409, odd columns




bessel_sequence_Jnu(nu=0.5,v=c(0.4,0.44,0.55))
Documentation reproduced from package gsl, version 1.2-20, License: GPL

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