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# Module pec

source code

Module for the pseudo-elliptical functions.

 Functions
int
 factorial(n) Return n! source code
float
 pec(x, y) The 2D pseudo-elliptic cosine function. source code
 Variables
__package__ = `'lib.geometry'`

Imports: pi

 Function Details

### factorial(n)

source code

Return n!

Parameters:
• `n` (int) - The number to return the factorial of.
Returns: int
n!

### pec(x, y)

source code

The 2D pseudo-elliptic cosine function.

This is defined as:

```   int_-pi^pi (1 - cos(theta_max)).dphi,
```

where:

```   theta_max = 1 / sqrt(cos**2(phi)/x**2 + sin**2(phi)/y**2).
```

The function is approximated as:

```           _inf
\        (-1)**n
2*pi*x*y >  ----------------- fn(x, y),
/___ 4**n * (2n + 2)!
n=0
```

and where the individual functions are:

```   n: 0; fn(x,y) = 1
n: 1; fn(x,y) = 2*a + 2*b
n: 2; fn(x,y) = 6*a^2 + 4*a*b + 6*b^2
n: 3; fn(x,y) = 20*a^3 + 12*a^2*b + 12*a*b^2 + 20*b^3
n: 4; fn(x,y) = 70*a^4 + 40*a^3*b + 36*a^2*b^2 + 40*a*b^3 + 70*b^4
n: 5; fn(x,y) = 252*a^5 + 140*a^4*b + 120*a^3*b^2 + 120*a^2*b^3 + 140*a*b^4 + 252*b^5
n: 6; fn(x,y) = 924*a^6 + 504*a^5*b + 420*a^4*b^2 + 400*a^3*b^3 + 420*a^2*b^4 + 504*a*b^5 + 924*b^6
n: 7; fn(x,y) = 3432*a^7 + 1848*a^6*b + 1512*a^5*b^2 + 1400*a^4*b^3 + 1400*a^3*b^4 + 1512*a^2*b^5 + 1848*a*b^6 + 3432*b^7
n: 8; fn(x,y) = 12870*a^8 + 6864*a^7*b + 5544*a^6*b^2 + 5040*a^5*b^3 + 4900*a^4*b^4 + 5040*a^3*b^5 + 5544*a^2*b^6 + 6864*a*b^7 + 12870*b^8
n: 9; fn(x,y) = 48620*a^9 + 25740*a^8*b + 20592*a^7*b^2 + 18480*a^6*b^3 + 17640*a^5*b^4 + 17640*a^4*b^5 + 18480*a^3*b^6 + 20592*a^2*b^7 + 25740*a*b^8 + 48620*b^9
n: 10; fn(x,y) = 184756*a^10 + 97240*a^9*b + 77220*a^8*b^2 + 68640*a^7*b^3 + 64680*a^6*b^4 + 63504*a^5*b^5 + 64680*a^4*b^6 + 68640*a^3*b^7 + 77220*a^2*b^8 + 97240*a*b^9 + 184756*b^10
n: 11; fn(x,y) = 705432*a^11 + 369512*a^10*b + 291720*a^9*b^2 + 257400*a^8*b^3 + 240240*a^7*b^4 + 232848*a^6*b^5 + 232848*a^5*b^6 + 240240*a^4*b^7 + 257400*a^3*b^8 + 291720*a^2*b^9 + 369512*a*b^10 + 705432*b^11
```
Parameters:
• `x` (float) - The theta_x cone angle (in rad).
• `y` (float) - The theta_y cone angle (in rad).
Returns: float
The approximate function value.

 Generated by Epydoc 3.0.1 on Fri Jun 14 11:29:06 2019 http://epydoc.sourceforge.net