BesselFunctions | R Documentation |
A collection and description of special mathematical
functions which compute the modified Bessel functions
of integer order of the first and second kind as well
as their derivatives.
The functions are:
BesselI | modified Bessel function of the 1st Kind, |
BesselDI | its derivative, |
BesselK | the modified Bessel function of the 3nd Kind, |
BesselDK | its derivative. |
BesselI(x, nu, expon.scaled = FALSE) BesselK(x, nu, expon.scaled = FALSE) BesselDI(x, nu) BesselDK(x, nu)
expon.scaled |
a logical; if TRUE, the results are exponentially scaled. |
nu |
an integer value greater or equal to zero, the integer order of the modified Bessel function. |
x |
a positive numeric value or a vector of positive numerical values. |
The functions return the values of the selected special mathematical function.
Diethelm Wuertz for the Rmetrics R-port.
Abramowitz M., Stegun I.A. (1972); Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing, New York, Dover Publishing.
Weisstein E.W. (2004); MathWorld – A Wolfram Web Resource, http://mathworld.wolfram.com
## Bessel I0 and K0 - # Abramowitz-Stegun: Table 9.8, p. 416-422 x = c(0.0, 0.01, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50) data.frame(x, I = exp(-x)*BesselI(x, 0), K = exp(x)*BesselK(x, 0)) # Compare with R's internal function: # data.frame(x, ratio = BesselI(x, 0) / besselI(x, 0)) # data.frame(x, ratio = BesselK(x, 0) / besselK(x, 0)) ## x = 0: c(BesselI(0, 0), BesselI(0, 1), BesselI(0, 2), BesselI(0, 5)) # Compare with R's internal function: # c(besselI(0, 0), besselI(0, 1), besselI(0, 2), besselI(0, 5)) c(BesselK(0, 0), BesselK(0, 1), BesselK(0, 2), BesselK(0, 5)) # Compare with R's internal function: # c(besselK(0, 0), besselK(0, 1), besselK(0, 2), besselK(0, 5)) ## Bessel I2 and K2 - # Abramowitz-Stegun: Table 9.8, p. 416-422 x = c(0.0, 0.01, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50) data.frame(x, I = BesselI(x, 2)/x^2, K = BesselK(x, 2)*x^2) # Compare with R's internal function: # data.frame(x, ratio = BesselI(x, 0) / besselI(x, 0)) # data.frame(x, ratio = BesselK(x, 0) / besselK(x, 0)) # data.frame(x, ratio = BesselI(x, 1) / besselI(x, 1)) # data.frame(x, ratio = BesselK(x, 1) / besselK(x, 1)) # data.frame(x, ratio = BesselI(x, 5) / besselI(x, 5)) # data.frame(x, ratio = BesselK(x, 5) / besselK(x, 5)) # data.frame(x, ratio = BesselI(x,50) / besselI(x,50)) # data.frame(x, ratio = BesselK(x,50) / besselK(x,50))
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