# Theories common to all applications¶

## Polynomial¶

### Summary¶

Fit a polynomial of degree $$n$$ to the data

• Function
$y(x) = \sum_{i=0}^n A_i x^i$
• Parameters
• $$n$$: degree of the polynomial function.

• $$A_i$$: polynomial coefficeints.

## Power Law¶

### Summary¶

Fit a power law to the data

• Function
$y(x) = a x^b$
• Parameters
• $$a$$: prefactor.

• $$b$$: exponent.

## Exponential¶

### Summary¶

Fit a single exponential decay to the data

• Function
$y(x) = a \exp(-x/T)$
• Parameters
• $$a$$: prefactor.

• $$T$$: exponential “time” constant.

## Double Exponential¶

### Summary¶

Fit two single exponential decay to the data

• Function
$y(x) = a_1 \exp(x/T_1) + a_2 \exp(-x/T_2)$
• Parameters
• $$a_1$$, $$a_2$$: prefactors.

• $$T_1$$, $$T_2$$: exponential “time” constants.

## Algebraic Expression¶

### Summary¶

Fit a user algebraic expression with $$n$$ parameters.

The expression can contain any of the following mathematical functions: sin, cos, tan, arccos, arcsin, arctan, arctan2, deg2rad, rad2deg, sinh, cosh, tanh, arcsinh, arccosh, arctanh, around, round, rint, floor, ceil,trunc, exp, log, log10, fabs, mod, e, pi, power, sqrt

It is the responsability of the user to input functions that make mathematical sense.

• Function
$y(x) = f({A_i}, x, F_{params})$
• Parameters
• $$n$$: number of parameters.

• $$A_i$$: coefficeints of the algebraic expression