Francis J. O'Brien, Jr.
Applied Math., Engineering, Algonquian Studies
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About me
My docs were deleted inadvertently for about 2 weeks. They were restored on 4 June 13! |||| Scientist, inventor & writer. Employed by US Govt., Naval Station Newport. RI native. Veteran, USAF. Ph.D. Columbia. Former President, Aquidneck Indian Council. Website lists publications in (1) Algonquian Studies (2) math./stat. (3) poetry (4) essays. Latest books: (a) 500 Integrals (DocStore) and (b) A Cultural History of the Native Peoples of Southern New England (Bauu Press). Recent book is Understanding Indian Place Names in Southern New England (on Amazon) Cheers! e-mail: francis.j.obrien@navy.mil francis28@cox.net
My Stats:
Docs: 12
Views: 52328
Profile Visits: 14568
Professional Information:
company: US Navy
title: Scientist & Diversity Program Manager
industry: Defense & Space
city: Newport
state: RI, zip: 2840
country: United States
undergraduate: RI College
degree: B.A. (Philo)
year: 1973
graduate: Teachers College & Grad. Sch Arts & Sciences, Columbia
degree: M.A., M.Phil., Ph.D.
year: 1980

Proof that lim(n-> inf) x^n/n!=0 by Stirling’s Approximation for Factorials (Part II)
From: waabu | Date: 11/24/2012  | Views: 115

A Note is added to the original paper. An additional simpler proof of the limit is given. more>>

115 views language: English
Derivative of exp(x^n) by limit definition
From: waabu | Date: 11/27/2012  | Views: 1217

We seek to provide a plausible elementary proof outline of derivative by the limit definition. This demonstration is not available in standard... ...  more>>

1,217 views language: English
Integral x^m exp(-Bx^n) and Related integrals. 2nd ed
From: waabu | Date: 1/3/2013  | Views: 117

Four related algebraic exponential formulas in Gradshteyn and Rhyzik are derived. Shows method of deriving integrals by "inspired guessing" and... ...  more>>

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A general limit for exponentials
From: waabu | Date: 3/14/2013  | Views: 661

In this paper we demonstrate a general limit for exponential functions by elementary differential calculus methods (log differentiation and... ...  more>>

661 views language:
A family of algebraic-exponential formulas
From: waabu | Date: 3/26/2013  | Views: 46

The author has created a small family of generalized indefinite and definite algebraic–exponential real variable integrals based on the gamma... ...  more>>

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Exponential Circular Integrals
From: waabu | Date: 6/21/2013  | Views: 3067

Demonstrates the evaluation of complicated algebraic-exponential-circular integrals by elementary complex numbers (Euler's Formula, DeMoivre's... ...  more>>

3,067 views language:
Expansion of ln(a + x) and the Binomial Series
From: waabu | Date: 6/24/2013  | Views: 127

A derivation of the expansion of ln(a x) by the Binomial Series. ERRATA: page 3, 3rd line: change "small h or" to "small h or large n" ERRATA:... ...  more>>

127 views language: English
Reading Comprehension Among Black American English Speakers
From: waabu | Date: 7/1/2013  | Views: 50

Despite my field & interest being statistics Columbia requested that I do this field work among Rikers Island felons. Was resentful about this... ...  more>>

50 views language: Japanese
Euler’s Formula by Series Expansions
From: waabu | Date: 7/4/2013  | Views: 80

This paper verifies Euler’s Formula by series expansions and graphical methods at an elementary level. Binomial and Exponential series expansions... ...  more>>

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Identities for Cosine cos^n(x) and Sine sin^n(x) by Complex Numbers
From: waabu | Date: 8/24/2013  | Views: 140

Derivation for powers of trigonometric functions (cosine and sine) using complex numbers. NOTE : Equations still garbled in places, but reads... ...  more>>

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