Comment says "from 2 to value / 2" however the code uses a loop that goes all of the way up to value. I updated the logic to be more consistent with the comment above it.

First and foremost, it's amazing to see a 14 year old writing a library. Keep up the good work, this is a great beginning! I hope this project gets traction, it could be very useful for school/college students for their maths assignment.

In terms of the code, there are a few ways you could improve them. Making a polynomial class is probably more efficient and scalable than writing a function for every degree.

How to write such class can be found at https://www.python-course.eu/polynomial_class_in_python.php

TLDR : See the code below (taken from the page above)

import numpy as np
import matplotlib.pyplot as plt


class Polynomial:
 

    def __init__(self, *coefficients):
        """ input: coefficients are in the form a_n, ...a_1, a_0 
        """
        self.coefficients = list(coefficients) # tuple is turned into a list

        
    def __repr__(self):
        """
        method to return the canonical string representation 
        of a polynomial.
   
        """
        return "Polynomial" + str(self.coefficients)

    
    def __call__(self, x):    
        res = 0
        for coeff in self.coefficients:
            res = res * x + coeff
        return res 

    
    def degree(self):
        return len(self.coefficients)   

    
    def __add__(self, other):
        c1 = self.coefficients[::-1]
        c2 = other.coefficients[::-1]
        res = [sum(t) for t in zip_longest(c1, c2, fillvalue=0)]
        return Polynomial(*res)

    
    def __sub__(self, other):
        c1 = self.coefficients[::-1]
        c2 = other.coefficients[::-1]
        
        res = [t1-t2 for t1, t2 in zip_longest(c1, c2, fillvalue=0)]
        return Polynomial(*res)
 

    def derivative(self):
        derived_coeffs = []
        exponent = len(self.coefficients) - 1
        for i in range(len(self.coefficients)-1):
            derived_coeffs.append(self.coefficients[i] * exponent)
            exponent -= 1
        return Polynomial(*derived_coeffs)

    
    def __str__(self):
        
        def x_expr(degree):
            if degree == 0:
                res = ""
            elif degree == 1:
                res = "x"
            else:
                res = "x^"+str(degree)
            return res

        degree = len(self.coefficients) - 1
        res = ""

        for i in range(0, degree+1):
            coeff = self.coefficients[i]
            # nothing has to be done if coeff is 0:
            if abs(coeff) == 1 and i < degree:
                # 1 in front of x shouldn't occur, e.g. x instead of 1x
                # but we need the plus or minus sign:
                res += f"{'+' if coeff>0 else '-'}{x_expr(degree-i)}"  
            elif coeff != 0:
                res += f"{coeff:+g}{x_expr(degree-i)}" 

        return res.lstrip('+')    # removing leading '+'

Fixed an import error and fleshed out ArithmeticSeries and GeometricSeries classes. This could be a good demo for generators, class methods and inheritance for you. :)

I have added a new file for series, which you can use to implement sin, cosine series, arithmetic, geometric, harmonic etc. types of series, and I have also added a polynomial class which I talked about in my reddit post. I have made comments that might help you understand classes a bit. Please feel free to contact me if you face any issues. Best of luck and keep it up !!