How were the other Hermite basis functions decided on? The ease function seems like an intuitive idea for something in real life starting and stopping nicely, and H0(t) seems to be a reflection of that.
I found this resource (https://coast.nd.edu/jjwteach/www/www/60130/New%20Lecture%20Notes_PDF/CE60130_Lecture%208%20with_footer-v04.pdf) that went into it a little bit, but it seems to just be mathematical phenomena that can be physically interpreted.
How were the other Hermite basis functions decided on? The ease function seems like an intuitive idea for something in real life starting and stopping nicely, and H0(t) seems to be a reflection of that.
I found this resource (https://coast.nd.edu/jjwteach/www/www/60130/New%20Lecture%20Notes_PDF/CE60130_Lecture%208%20with_footer-v04.pdf) that went into it a little bit, but it seems to just be mathematical phenomena that can be physically interpreted.