Hi, guys.

Let d := e^(1/e).

Facts:

1. a(n) := d + 1/n, Lim n->inf a(n)[4]n = inf.

2. b(n) := d + 1/n^2, Lim n->inf b(n)[4]n = e exists.

Questions:

1. Can be defined real function f(n,x) that c(n,x) := d + f(n,x), and Lim n->inf c(n,x)[4]n = l(x) exists, and e < l < inf?

2. For which x function l(x) can be defined?

3. How "good" functions f(n,x) and l(x) can be relative to x?

4. How function l(x) relates to tetration definition given by D.Kuznetsov in collaboration with you?

5. If l(x) can be defined, can be it used to give yet another definition of tetration for real positive heights (analogy with classics)?

Let d := e^(1/e).

Facts:

1. a(n) := d + 1/n, Lim n->inf a(n)[4]n = inf.

2. b(n) := d + 1/n^2, Lim n->inf b(n)[4]n = e exists.

Questions:

1. Can be defined real function f(n,x) that c(n,x) := d + f(n,x), and Lim n->inf c(n,x)[4]n = l(x) exists, and e < l < inf?

2. For which x function l(x) can be defined?

3. How "good" functions f(n,x) and l(x) can be relative to x?

4. How function l(x) relates to tetration definition given by D.Kuznetsov in collaboration with you?

5. If l(x) can be defined, can be it used to give yet another definition of tetration for real positive heights (analogy with classics)?