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Some solutions[edit]

Please specify some discrete solution. This will help the reader to check whether some function available in some program may be the function this article is talking about. Tomeasy T C 07:58, 21 July 2009 (UTC)

I don't understand what you mean by discrete solution. --Zvika (talk) 09:20, 21 July 2009 (UTC)
The values for, e.g., Q(0) or Q(1) or even Q(0.5). Tomeasy T C 17:56, 21 July 2009 (UTC)
Ah, that's a good idea. Will do. --Zvika (talk) 04:33, 22 July 2009 (UTC)


There is an improved bound for Q(x), given at [1]:

  Q(x) \approx \varphi(x)\bigg(\frac{1}{x} - \frac{1}{x^3} + \frac{1\cdot3}{x^5} - \frac{1\cdot3\cdot5}{x^7} + \frac{1\cdot3\cdot5\cdot7}{x^9} + \cdots\bigg),

where each partial sum gives either upper or lower bound, depending on the sign of the last summand. The sum itself is divergent however, so it cannot be used to calculate the integral with arbitrary precision.

Another approximation due to Laplace:

  Q(x) = \frac{\varphi(x)}{x + \frac{1}{x + \frac{2}{x + \frac{3}{x + \frac{4}{x + \ldots}}}}}

 … stpasha »  19:09, 1 October 2009 (UTC)

Sounds interesting and worthy of inclusion, if you can find a RS for it. --Zvika (talk) 18:19, 3 October 2009 (UTC)
I just noticed that the bounds given in the article correspond to Laplace’s continuous fraction terminated at k=0 and k=1 respectively:

    Q(x)\approx \frac{\varphi(x)}{x} \quad \text{and} \quad Q(x)\approx \frac{\varphi(x)}{x+\frac{1}{x}}
But you're right, a reliable source which attributes second formula to Laplace would be nice to have.  … stpasha »  18:45, 3 October 2009 (UTC)


In the second paragraph of the article, shouldn't the eta be a mu? -- UKoch (talk) 15:11, 24 February 2014 (UTC)

Yes, it should be a mu, and \varphi(x) should be \phi(x), to be consistent with the notation on the Normal Distribution page. I will fix this. David C Bailey (talk) 08:06, 21 November 2014 (UTC)
Thanks! -- UKoch (talk) 17:57, 23 November 2014 (UTC)