I have numpy array and I want to use power series like taylor series of `e^x`, and I am wondering how to implement this in python. For the simplicity purpose, I think I can use maclaurin series at `x0=0`, wheres `x` is numpy array. Basically, I have 1 dim pixel vector, and I want to non-linearly expand each pixel value by using taylor series expansion of e^x. In other words, in output vector, each pixel will be replaced with first and second term of taylor series expansion term. Any idea to make this happen in python?

**mathematical concept**:

here is the simple math concept I want to accomplish, wheres nunmpy array is expected to be non-linearly expanded by using power series like maclaurin series of `e^x`.

[![enter image description here](https://i.stack.imgur.com/sLr0C.jpg)](https://i.stack.imgur.com/sLr0C.jpg)

**my attempt**:

```
import numpy as np

arr= np.array([[120.0,24.0,12.0],[14.0,28.0,43.0]])
arr= arr/255.0

def maclurin_exp(x, power):
    res = x*0
    for i in range(power):
      res += x**i/math.factorial(i)
    return res

## test my code:
maclurin_exp(x=arr, power=3)

```

**new update 2**:

Precisely, `F` is taylor series of `e^x`, `x` is each pixel value, `x0` is approximation point at 0. For example if we have 8 pixel in 1 dim vector, then after we used taylor series of e^x for each pixel value, first and second term of taylor expansion will be considered as ouput.

[![enter image description here](https://i.stack.imgur.com/plAvA.jpg)](https://i.stack.imgur.com/plAvA.jpg)

how do I make this happen in python? any workaround to accomplish the implementation of Maclaurin series for `e^x` in more compact way? any thought?

**expected output**

for example we have 1 dim pixel vector `[1,2,3,4,5,6,7,8]`, then we apply above mathematical equation to approximate each pixel value by using maclurin series of e^x:

```
pixel = [1,2,3,4,5,6,7,8]

```

then first and second term of taylor series of e^x for each pixel value would be my final output.