# einsteinF: Einstein Functions

Description Usage Arguments Details Value Examples

### Description

Einstein functions.

### Usage

 1 einsteinF(d, x)

### Arguments

 x numeric or complex vector. d parameter to select one of the Einstein functions E1, E2, E3, E4.

### Details

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....

### Value

Numeric/complex scalar or vector.

### Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ## 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() ## End(Not run)

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