(09/13/2014, 11:49 PM)jaydfox Wrote: ...and comparing your power series, it easily follows that your power series is asymptotic to exp(x) x^(1/2). Hmm, oh dear, I think you missed a +1 in the Gamma function in your series? (LOL, it's okay, I usually forget the +1 as well.) If you set beta=-1/2, then all is well!

Haha, I think my math is wrong somewhere, because I double-checked in Excel, and you were right! I obviously did something wrong in my math, though I haven't figured out what yet... I'll update this post when I get it sorted out, LOL!

Update: I think I figured it out. I was doing the Gamma function correctly (beta = -1/2), but I was extracting beta from the exponent incorrectly. I had my equations backwards. So my original equation (with the beta's intact) is still correct... I think...

And generally:

~ Jay Daniel Fox