General Mathematics

    

Gelfond's Constant Using MKB Constant Like Integrals.

Authors: Marvin Ray Burns

First we will follow the path the author took to find out that for integral(cos[pi*I*x]x^(1/x),{x,1,a}) and integral(sin[pi*I*x]x^(1/x),{x,1,a}), the limit of the ratio of a to a-1,as a goes to infinity is Gelfond's Constant, (e^pi). We will consider that the hypothesis and provide hints for a proof using L'Hospital's Rule (since we have indeterminate forms as a goes to infinity). We find we there is no limit of the ratio of the previous forms of integrals when the "I" is left out, and give a small proof for them.

Comments: 10 Pages.

Download: PDF

Submission history

[v1] 2016-09-05 18:30:15
[v2] 2016-09-07 15:48:30
[v3] 2016-09-11 20:28:10
[v4] 2016-09-13 19:42:46
[v5] 2016-09-15 19:17:54

Unique-IP document downloads: 592 times

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