Einstein Functions
Einstein functions.
einsteinF(d, x)
x |
numeric or complex vector. |
d |
parameter to select one of the Einstein functions E1, E2, E3, E4. |
The Einstein functions are sometimes used for the Planck-Einstein oscillator in one degree of freedom.
The functions are defined as:
E1(x) = \frac{x^2 e^x}{(e^x - 1)^2}
E2(x) = \frac{x}{e^x - 1}
E3(x) = ln(1 - e^{-x})
E4(x) = \frac{x}{e^x - 1} - ln(1 - e^{-x})
E1 has an inflection point as x=2.34694130....
Numeric/complex scalar or vector.
## Not run:
x1 <- seq(-4, 4, length.out = 101)
y1 <- einsteinF(1, x1)
plot(x1, y1, type = "l", col = "red",
xlab = "", ylab = "", main = "Einstein Function E1(x)")
grid()
y2 <- einsteinF(2, x1)
plot(x1, y2, type = "l", col = "red",
xlab = "", ylab = "", main = "Einstein Function E2(x)")
grid()
x3 <- seq(0, 5, length.out = 101)
y3 <- einsteinF(3, x3)
plot(x3, y3, type = "l", col = "red",
xlab = "", ylab = "", main = "Einstein Function E3(x)")
grid()
y4 <- einsteinF(4, x3)
plot(x3, y4, type = "l", col = "red",
xlab = "", ylab = "", main = "Einstein Function E4(x)")
grid()
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