F.22 Functions — Folios

Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.22 (Functions) (SeeligNotebooks).

Folio 0130 (Page 1 of 2): Gaussian CDF Phi(x), Q(x), erf(x) & Abramowitz–Stegun Eq. 7.1.26

[Folio 0130]

Folio 0130 (original scan 0130.jpg) from resources/seelig/22_functions.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0130 (0130.jpg, Sheet 1 of 2):

Defines \(\Phi(x), Q(x), \operatorname{erf}(x), \operatorname{erfc}(x)\) and lists the 6 numerical constants \(p, a_1..a_5\) from AMS-55, p. 299.

\[\Phi(x) = \frac{1}{2} + \frac{1}{2}\operatorname{erf}\left(\frac{x}{\sqrt{2}}\right), \qquad \operatorname{erf}(x) \approx 1 - \left(\sum_{k=1}^5 a_k t^k\right) e^{-x^2}, \quad t = \frac{1}{1 + 0.3275911 x}\]

Editorial & Symbolic Notes

Archival scan 0130.jpg from Fred W. Seelig’s notebook dossier on F.22 Functions (Page 1 of 2). Companion OpenDocument worksheet(s): General Reference.

Folio 0131 (Page 2 of 2): Six Discrete & Continuous Probability Distributions

[Folio 0131]

Folio 0131 (original scan 0131.jpg) from resources/seelig/22_functions.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0131 (0131.jpg, Sheet 2 of 2):

Summarizes formulas and density/CDF sketches for Binomial, Poisson, Bernoulli, Uniform, Exponential, and Normal distributions.

\[\Phi(x) = \frac{1}{2} + \frac{1}{2}\operatorname{erf}\left(\frac{x}{\sqrt{2}}\right), \qquad \operatorname{erf}(x) \approx 1 - \left(\sum_{k=1}^5 a_k t^k\right) e^{-x^2}, \quad t = \frac{1}{1 + 0.3275911 x}\]

Editorial & Symbolic Notes

Archival scan 0131.jpg from Fred W. Seelig’s notebook dossier on F.22 Functions (Page 2 of 2). Companion OpenDocument worksheet(s): General Reference.