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2d
comment Which polynomial has similar properties with Legendre?
Looking a bit more into it. Those aren't even polynomials. So the technique above doesn't apply. They are much more artificial (perhaps specially invented for some real life application). Do you want a proof of their orthogonality? Etc... They are orthogonal but they aren't polynomials and so asking how to construct them from polynomials won't make too much sense
2d
comment Which polynomial has similar properties with Legendre?
The tools above are overkill if that's your intention.
2d
comment Which polynomial has similar properties with Legendre?
Your link gives there general formula right there. Anyone should be able to find them. The proof of orthonormality is also given
2d
answered Solving the logistic equation
2d
comment Solving the logistic equation
Welcoming to math.stackexchange! It's usually recommended to include your own work in your quesiton so we can see where you got lost, and better help you.
2d
answered How can I solve this integral with the comparison theorem?
2d
answered Which polynomial has similar properties with Legendre?
2d
comment Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
But given my tiny shred of experimental evidence it appears that doesn't really change anything at all.
2d
comment Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
@MarianoSuárez-Alvarez the question you posted was very helpful but the responses often resorted to an argument such as: (1+1)(x+y) = (1+1)x + (1+1)y = (1)(x+y) + (1)(x+y). It occurred to me what I am asking is weaker than that as the only think I can derive from my axioms is (1+1)(x+y) = (1+1)x + (1+1)y, and no statement can be made about the nature of (1)(x+y) + (1)(x+y), at least not obviously. So my version of the distributive property is in some sense, much weaker than classical distributive, if you use hte functional equations i have given above.
2d
comment Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
@RobertLewis thanks again! I was going to use u and v at variables but since i had u as a function i figured that wouldn't be too pretty, forget to edit it out.
2d
revised Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
edited body
2d
comment Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
@RobertLewis, Thanks! I made the correction
2d
revised Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
edited body
2d
comment Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
@MarianoSuárez-Alvarez, haha I don't disagree with that, but, my methods weren't most efficient. So I made do with up to that order and then tried to make a conjecture :)
2d
comment Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
But what I'm getting at is more subtle than that. When I try to find rings that don't have abliean addition, my computer program verifies that no ring-like analogues exist. In a strict sense, having a second opeartion that distributes over the first, and carries its own unique identity, at least for small groups (I checked all groups up to order 6) yields no ring like objects with non abelian underlying groups
2d
revised Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
added 181 characters in body
2d
asked Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
Jun
27
asked Gomory's cut typical running time until the constraint is fractional
Jun
22
accepted How to Invert the Euler Lagrange Equations?
Jun
21
comment How to Invert the Euler Lagrange Equations?
Yes @Gregory that is the goal