I came up with the following Python code to permute a Hermite polynomial in the
fashion of the book I am going through (Analysis of Engineering Structures and
Material Behavior).
import numpy
# from numpy import polynomial
-----
if __name__ == "__main__":
n = 1
n = (n + 1)
hermite_n = ''
for i in range(n):
hermite_n += 'α'+str(i+1)+'x**'+str(i)+' + '
print(hermite_n)
-----
output:
α1x**0 + α2x**1 +
-----
So I am told to permute in said fashion for a first order hermite that the
author is using. So I read a bit in NumPy's documentation that there is some
class available for what are called Hermite's be it for physics or an "_E"
type. It seems that for physics I am being asked to enter a list of
coefficients but I'll admit that at this point I don't really know how the
coefficients would be entered to achieve a corresponding output of like kind
that I created above.
This is the permutation for a first order Hermite polynomial described by
the author:
(Pn(x)=\alpha _{1}+\alpha
_{2}x+\alpha_{3}x^2+...\alpha_{n+1}x^n=\sum_{i=0}^{n} \alpha _{i+1}x^i)
(https://latex.codecogs.com/)
So what I would like to do with NumPy is to achieve a full permutation of
the above described Hermite polynomial of a first order where n is described as
the order of the polynomial and the number of terms is said to be (n+1).
Incidentally there will be a second order (2D) Hermite shewn with a
different sigma sum notation used to permute it and also a third order (3D)
Hermite also shewn with a different sigma sum notation used to permute it that
I will have to cover maybe in a later discussion not to become over verbose
here. Is it possible that it can be explained to me how to achieve this and or
what would be the coefficients and or how to enter the coefficients for said 1D
problem and or how to achieve an identical permutation as talked about (as I
have enumerated from the author) with NumPy's Hermite system. If so what class
would I or should I use be it 'Hermite' or 'Hermite_E' from the NumPy library?
Thank you very much. Any help on this would be greatly appreciated!
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