May 12th, 2017, 10:57 am
Amin:I believe similar techniques can be used with some sets of orthogonal polynomials where we have relationships of the form
[$]H_a(x+y)=constant* H_b(x) H_c(y)[$]
For example hermite polynomials have some properties like this and also some similar umbral calculus related properties. There could be some general way of evaluating functions in the spirit of 'sliderule' evaluation of exponentials after representing the functions in terms of appropriate orthogonal polynomials. At least seems interesting to me.
I feel this property can have many more novel applications and it is very underestimated and that is why I thought I should mention it due to its relevance here.
You think life is a secret, Life is only love of flying, It has seen many ups and downs, But it likes travel more than the destination. Allama Iqbal
