Pandas' expanding with apply function on multiple columns

Is it possible to use panda's expanding function to calculate the coefficient of a polynomial regression using several columns of the window object?

I have a data frame which has two columns, a predictor and a response. I want to use pandas' expanding() function to calculate the corresponding coefficients of a second order polynomial regression for each expanding pair of series. For each row I would like to get the updated coefficients from the regression applied to all previous rows.

import pandas as pd
import numpy as np

def func1(df):
   # some processing
   return np.polyfit(df['Input'], df['Response'], 2)
   
def func2(x, y):
   # some processing
   return np.polyfit(x, y, 2)

np.random.seed(0)
df = pd.DataFrame(np.random.rand(10, 2).round(2), 
                  columns=['Input', 'Response'])

df[['Coef1', 'Coef2', 'Coef3']] = df.expanding(min_periods=3).apply(func)

I'd like the output to look like this:

>>> df

   Input Response Coef1  Coef2  Coef3
0  0.63  0.23     NaN    NaN    NaN
1  0.45  0.11     NaN    NaN    NaN
2  0.17  0.71     NaN    NaN    NaN
3  0.17  0.32     0.19   0.54   0.50
4  0.65  0.99     0.48   0.23   0.60
5  0.21  0.54     0.71   0.89   0.97
6  0.63  0.73     0.22   0.05   0.80
7  0.54  0.23     0.87   0.01   0.25
8  0.33  0.06     0.18   0.96   0.03
9  0.18  0.72     0.13   0.38   0.13

My different trials has led to two types of error. If I use the function that uses the dataframe as a parameter such as in df[['Coef1', 'Coef2', 'Coef3']] = df.expanding(min_periods=3).apply(func1)), I get KeyError: 'Input'. If I use the second function where I extract the parameters before df['Coef1', 'Coef2', 'Coef3'] = df.expanding(min_periods=3).apply(lambda x: func2(x['Input'], x['Output'])), I get DataError: No numeric types to aggregate However, If I try for instance df.expanding().cov(pairwise=True) it shows that calculation can be performed on the different columns of the object returned by expanding. There's a similar question here: Apply expanding function on dataframe. However, the solution consisting in calling expanding() in the function does not seem to apply in this case. I would appreciate any pointers or suggestion.

I found a package that does that with numpy: 3jane.github.io/numpy_ext so it inspired me to do it manually:

def func_np(df):
    length = len(df)
    if length == 1:
        return [[0], [0], [0]]

    coef1, coef2, coef3 = [], [], []

    x = df['A'].to_numpy()  # This is the predictor column
    y = df['B'].to_numpy()  # This is the response column

    for step in range(1, length + 1):
        weights = np.polyfit(x[: step], y[: step], 2)  # 2 is the polynomial's order
        coef1.append(weights[0])
        coef2.append(weights[1])
        coef3.append(weights[2])
    # Note that coef1, coef2, coef3 correspond to the polynomial terms from highest to lowest

    # It is easier to return a data frame, so that we can reassign the result to the initial one
    return pd.DataFrame({'Coef1': coef1, 'Coef2': coef2, 'Coef3': coef3})

I wanted to do it with Numba to speed up the execution but it does not recognize the np.polyfit function. Also I have not found a neat way to assign back the results to the initial data frame. That is why I am still interested in seeing a simple and more "pythonic" solution with expanding()