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James Van Allen journal, 1951?-December 1954
Page 83
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x _= 1 + [delta?] (a exponent x) = (a exponent (1 + [delta?])) = (a)(a exponent [delta?]) = a [ 1 + ([delta?]) (ln a) + (((([delta?])(ln a)) exponent 2)/(2!)) + . . . ] ----------------------------------------------------------------------- An interesting identity (well known, of course) Let y = (x exponent x) ln y = ((x)(ln x)) or y = (e exponenet ((x)(ln x))) therefore, [boxed below here:] (x exponent x) = (e exponent ((x)(ln x))) [boxed above here] Not restricted to base e More generally: (x exponent x) = (a exponent ((x)(log sub a)(x))) -------------------------------------------------------------- 6 September 1951 "The Energy Spectrum of Primary Cosmic Radiation" M. F. Kaplan, B. Peters, H. L. Reynolds, D. M. Ritson Authors' Abstract: "Techniques have been developed by which the energy spectrum of heavy primary nuclei can be measured
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x _= 1 + [delta?] (a exponent x) = (a exponent (1 + [delta?])) = (a)(a exponent [delta?]) = a [ 1 + ([delta?]) (ln a) + (((([delta?])(ln a)) exponent 2)/(2!)) + . . . ] ----------------------------------------------------------------------- An interesting identity (well known, of course) Let y = (x exponent x) ln y = ((x)(ln x)) or y = (e exponenet ((x)(ln x))) therefore, [boxed below here:] (x exponent x) = (e exponent ((x)(ln x))) [boxed above here] Not restricted to base e More generally: (x exponent x) = (a exponent ((x)(log sub a)(x))) -------------------------------------------------------------- 6 September 1951 "The Energy Spectrum of Primary Cosmic Radiation" M. F. Kaplan, B. Peters, H. L. Reynolds, D. M. Ritson Authors' Abstract: "Techniques have been developed by which the energy spectrum of heavy primary nuclei can be measured
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