I need the Laplace form of the second order B splines over logarithmically-spaced knot.
I have read a paper in which it is mentioned that ;
" Heaviside function can be represented as the sum of all b-splines with indices from negative to positive infinity which is called partition of unity property ".
Please look at the image attached ;
Zero-th first and second order B-spline with index zero
How can I write for example the second order B-spline with index 2,3 in terms of Heaviside function ?
I want to have the Laplace form of second order b-spline with indices from 0 to 4 which can be obtained easily if I can write B-spline with higher indices in terms of Heaviside function.
If you know any reference in this regards please introduce me.
Many thanks in advance , Ehsan