Alvaro: Double Barrier Formula Question

[Alvaro]

Hi everyone,

This is my first post here, and would like to thank to the comunity for let me be part of it.

I have a math question for Don about the first barrier formula on pag 136 of BJA3.

The second term of this formula contains an infinit serie.

I looked through my math book, seeking out if it serie is a kind of geometric or power serie, etc; to get the final sum, but I couldn't figure it out.

Thus the question is,

How can I get the sum of this serie?

Can I only approach the sum by adding term by term?

Thanks beforehand from Argentina.

Alvaro

[Norm Wattenberger]

> Thanks beforehand from Argentina.

Beautiful country.

Just from looking at the series, you can see it is obviously unusually complex. Afraid there is no way to calculate it other than calculating each step in the series and determining if it has converged to a point that is acceptable. Further, if the input to the formula is not fairly reasonable, the series will not converge at all, but will swing wildly. So, you need also check for this condition. You will also find that even when it does converge, the individual terms can have extreme magnitudes. When I first attempted to use the formula, I had a hard time believing it would work. But, sure enough, for rational inputs, the output is remarkably close to simulation.

Serious Blackjack Software

[Alvaro]

Norm,

First thanks for the reply.

> Afraid there is no way to calculate it other than calculating each step in the series and determining if it has converged to a point that is acceptable.

That was I wanted to know!

> even when it does converge, the individual terms can have extreme magnitudes.

I settled every terms on a spreadsheet and, I went encreased the sum, and as you said, certainly the values swing widely.

I have compared several entries with your online-formula and I've gotten the same values.So it seems to be correct.

thank you again from Argentina.
Alvaro