Talk:Lidstone series

Limits

Excerpt from the article:

$h(\theta ;f)=\lim \sup {\frac {1}{r}}\log |f(re^{i\theta })|\,$

is bounded above by t. Thus, the constant N used in the summation above is given by

$t=\lim \sup h(\theta ;f)\,$

The first limsup must have meant

$h(\theta ;f)={\underset {r\to {\text{something}}}{\lim \sup }}{\frac {1}{r}}\log |f(re^{i\theta })|\,$

and the second must have meant

$t={\underset {\theta \to {\text{something}}}{\lim \sup }}h(\theta ;f).\,$

What are the two "somethings"? Michael Hardy (talk) 02:13, 3 April 2009 (UTC)

Hi Micheal, The first something is \infty, as should be apparent from the article exponential type. The second should not be lim sup, but a simple sup over the interval theta in [0,2pi). linas (talk) 19:52, 3 April 2009 (UTC)

Got it. Thank you.

Next question: Who's Lidstone? Michael Hardy (talk) 05:46, 4 April 2009 (UTC)

OK, a guess: Could it be George James Lidstone, after whom Lidstone smoothing is named? Michael Hardy (talk) 05:50, 4 April 2009 (UTC)

.......and I find the answer here. Michael Hardy (talk) 05:54, 4 April 2009 (UTC)

So it would seem. FWIW, I did look; the book I have does not hint at who Lidstone was. linas (talk) 20:46, 21 April 2009 (UTC)