f[n_?EvenQ] := 1 + f[n/2]; 
f[n_?OddQ] := 1 + f[(n - 1)/2] + f[(n + 1)/2]; f[1] = 1;

BTW using the classroom assistant palette under Typesetting in the 5th row 4th entry you also find the standard brackets you need to do these statements. The result is this:

This looks like standard typesetting and works just fine:

v[2^-# &]

(*convergent*)

Cheers,

Marco

If you convert this to standard form it gives you yet another way of writing the same thing:

v[a_] := Piecewise[{
    {"convergent", Limit[a[n + 1]/a[n], n -> \[Infinity]] < 1}, 
    {"divergent", Limit[a[n + 1]/a[n], n -> \[Infinity]] > 1}, 
    {"indeterminate", Limit[a[n + 1]/a[n], n -> \[Infinity]] == 1}}]

I think you may have to convert your problem into a system of two equations for RSolve to be able to handle it. Something like x = n/2 for the even numbers and y = (n-1)/2 for the odd numbers.

Apologies for the fury of replies to my little question. I've been trying (in vain) to find a picture or link to illustrate my point. The closest I can come is the following:

Suppose I'd like to type the alternate statement of D'Alembert's ratio test (see 1.6 in Mathematical Methods for Physicists by Arfken et al, 7th edition) in traditional form (i.e. the big left curly brace with conditions to the right). How can I do this in Mathematica?

Thanks,

Dean Sparrow

I mean an equation that has a certain output depending on a given input

That is normally called a function, not an equation. If you can give an example of what you mean or trying to code, it will make it easier to help you.

In words, let a(n) be terms of an infinite series. If, in the limit as n approaches infinity, a(n+1)/a(n) < 1, then the series is convergent. Similarly if the ratio is > 1, then it is divergent. If the ratio = 1 however, then the test is inconclusive.

I just want to type this "pretty", like a textbook.

Thanks.

Thanks, Marco - problem solved.

Frank, this latest edition has swollen to 1200 pages. Amazon shows a pared-down version entitled Essential Methods for Physicists.

Best,

Dean