This image below shows a few lines from the July 1948 Bell System Technical Journal.
The 'p' character in the second line, used to typeset the "p0 = p1 = 1/2" equation is the character in question. The entire document should be available as a PDF here (14Mb). That particular equation is on page 29 of the PDF, but it is used in equations throughout.
I've tried WhatTheFont on both the isolated character and a bit of running text, and didn't get anything sensible. (I can't post the links to the images I submitted because my reputation is too low). The biggest problem is that the character is used only in equations and not in the running text. Sometimes there are special math characters for equations but usually it's just the italic version of the font. I'm hoping the way the top of the character extends so far past the stem will make it easier to identify.
Ideally I could find a (nearly) matching italic font from this LaTex catalogue, but just getting a name would be a great help too.