MATHEMATICAL
PUBLICATIONS
April 26, 2013
Thomas J Osler
1. Leibniz rule for fractional derivatives generalized and an application
to infinite
series, SIAM J. Appl. Math., 18 (1970), pp. 658-674. MR 41#5562
(download from JSTOR) download PDF file
2. The fractional derivative of a composite function, SIAM J. Math.
Anal, 1 (1970),
pp. 288-293. MR 41#5563 download PDF file
3.
Math. Anal. 2 (1971), pp. 37-48. MR 45#3682 download PDF file
4. Fractional derivatives and leibniz
rule, Amer. Math. Monthly, 78 (1971),
pp. 645-649. (download from JSTOR) download PDF file
5. A further extension of Leibniz rule to fractional derivatives and its relation to Parseval’s formula, SIAM J. Math. Anal., 3 (1972), pp. 1-16. MR 48#2323a download PDF file
6. An integral analogue of
transforms, Math. Comp., 26 (1972), pp. 449-460. MR
46#5950. download
PDF file
7. The integral analog of the Leibniz rule, Math. Comp., 26 (1972),
pp. 903-915.
MR 47#2792. download PDF file
8. A correction to Leibniz rule for fractional derivatives, SIAM J. Math. Anal., 4 (1973), pp. 456-459. MR 48#2323b download PDF file
9. Differences of arbitrary order (With J. B. Diaz), Math. Comp., 28
(1974),
pp. 185-202. MR 49#11077 (download from JSTOR) download PDF file
10. Fundamental properties of fractional derivatives via Pochhammer integrals.(With J.
L. Lavoie and R. Tremblay). A paper in "Fractional Calculus and Its
Applications" edited by B. Ross, Springer-Verlag,
New York, 1975, pp. 323-356.
MR 57#16490
11. Open questions for research. (Proc. Internat.
Conf. Univ.
Haven
12. An indentity for simplifying certain generalized hypergeometric functions, Math Comp., 29 (1975), pp. 888-893. MR 51#10710 download PDF file
13. Leibniz rule for fractional derivatives used to generalize formulas of Walker and Cauchy, Bul. Inst. Polit, Jasi, 21-(25), 1-2, (1975), pp. 21-24. MR 52#8822 download PDF file
14. Fractional derivatives and special functions, SIAM Review, 18
(1976),
pp. 240-268. MR 53#13666 download PDF
file
15. A quick look at Lyapunov space,
Mathematics and Computer Education,
28 (1994), pp. 183-197.
16. A mathematical art exhibit, Mathematics and Computer Education,
29 (1995),
pp. 245-252.
17. Get billions and billions of digits of pi from a wrong formula, Mathematics and Computer Education , Vol. 33, No. 1, 1999, pp.40-45. download PDF version
18. The trinomial triangle, (with James Chappell, student), The College Mathematics Journal, Vol. 30, No. 2, 1999, pp. 141-142. download PDF version
19. Extending the Babylonian algorithm, Mathematics and Computer Education, Vol. 33, No. 2, 1999, pp. 120-128. download PDF version
20. The tautochrone under arbitrary potentials using fractional derivatives, (with Eduardo Flores), American Journal of Physics, (Am. J. Phys.), 67(1999), pp. 718- 722. download PDF version
21. The united Vieta’s and Wallis’s products for pi, American Mathematical Monthly, 106 (1999), pp. 774-776. download PDF version
22. Fractal Movies, Mathematics and Computer Education, Vol. 33 (1999), pp. 236-243. download PDF version
23. A child’s garden of fractional derivatives, (with Marcia Kleinz), The College Mathematics Journal, Vol. 31, No. 2, (2000), pp. 82-887 download PDF version
24. The binomial to binomial theorem, The College Mathematics Journal, Vol. 31, No. 3, (2000), pp. 211-212. download PDF version
25. Spacetime numbers the easy way, (with Nick Borota and Eduardo Flores), Mathematics and Computer Education, Vol. 34, No. 2, (2000), pp. 159-168. download PDF version
26. Playing with partitions on the computer, (with Abdul Hassen), Mathematics and Computer Education , Vol. 35, No. 1, (2001), pp. 5-17. download PDF version
27. Mutations of the Mandelbrot set, (with Jae Hattrick-Simpers, student), Mathematics and Computer Education, Vol. 35, No. 1, (2001), pp. 18-26. download PDF version
28. The remarkable incircle of a triangle. (with Ira Fine), Mathematics and Computer Education, Vol. 35, No. 1, (2001), pp. 44-50. download PDF version
29. Cardan polynomials and the reduction of radicals, Mathematics Magazine, Vol 47, No. 1, (2001), pp. 26-32. download PDF version
30. The rotating tautochrone, (with Eduardo
Flores), Journal of Applied Mechanics,
68(2001), pp. 353-356. download
PDF version
31. Rearranging terms of a harmonic-like series, Mathematics and Computer Education, 35(2001), pp. 136-139. download PDF version
32. Fun with 0.999... , The AMATYC Review, 22(2001), pp. 53-56. download PDF version
33. An unusual approach to Kepler’s first law, American Journal of Physics, 69(2001), pp. 1036-8. download PDF version
34. An unusual view of the ellipse, Mathematics and Computer Education, 35,(2001), pp. 234-236. download PDF version
35. Variations on Vieta’s and Wallis’s products for pi, (with Michael Wilhelm), Mathematics and Computer Education, 35(2001), pp. 225-232. download PDF version
36. A tale of two series, (with Marcus Wright), The College Mathematics Journal, 33(2002), pp. 99-106. download PDF file
37. Divergence of the harmonic series, p series and others by rearrangement, (with Bernard August, Emeritus), The College Mathematics Journal, 33(2002), pp. 233-4. download PDF version
38. Fermat’s little theorem from the multinomial theorem, The College Mathematics Journal, 33(2002), p. 239. download PDF version
39. A table of the partition function, (with Abdul Hassen and T. R. Chandrupatla), The Mathematical Spectrum, 34(2001/2002), pp. 55-57. download PDF version
40. Visual Basic for QuickBasic Programmers, (with Seth Bergmann and T. R. Chandrupatla), Mathematics and Computer Education, 36(2002), pp. 133-138. download PDF file
41. Functions of a spacetime variable, (with Nicolae A. Borota), Mathematics and Computer Education, 36(2002), pp. 231-239. Download PDF file
42. An easy introduction to biplex numbers, (with Dipti Bardhan), Mathematics and Computer Education, 36(2002), pp. 278-286. Download PDF file
43. An easy look at the cubic formula, Mathematics and Computer Education, 36(2002), pp. 287-290. Download PDF file
44. Proof without words: Integral of sine squared, The AMATYC Review, 24(2002), p. 65. Download PDF file
45. A computer hunt for Apery's constant, (with Brian Seaman), Mathematical Spectrum, 35(2002/2003), No.1, pp. 5-8. Download PDF file
46. A magic trick from Fibonacci, (with James Smoak), The College Mathematics Journal, 34(2003), pp. 58-60. Download PDF file
47. Variations on a theme from Pascal's triangle, The College Mathematics
Journal, 34(2003), pp. 216-223. Download PDF file
48. Visual proofs of two integrals, The College Mathematics Journal, 34(2003), p.231-232.. Download PDF file
49. An unusual product for sin z and variations of Wallis’s product, The Mathematical Gazette, 87(2003), pp. 134-139. Download PDF file
50. Finding Zeta(2p) from a product of sines. The American Mathematical Monthly, 111(2004),
pp. 52-54. Download
(PDF) original version containing motivational material.
Download (PDF) final accepted version (more
formal with less motivation)
51. Another intuitive approach to
52. Geometric construction of Pythagorean triangles, (with Tirupathi
R. Chandrupatla), Mathematics and Computer Education, 38(2004), pp. 90-91.
Download PDF file
53. Variations on the linear first order ODE, (with Brian Seaman), International Journal of Mathematical Education in Science and Technology, 35(2004), pp.309-315. Download (PDF) version.
54. Extending Theon's ladder to any square root, (with Shaun Giberson), The College Mathematics Journal, 35(2004), pp. 222-226. Download PDF file
55. Problems on divisibility of binomial coefficients, (with James Smoak). The AMATYC Review, 25(2004), pp. 17-21.Download PDF file.
56. Generalizing integrals involving x^x and series involving n^n, (with Jeffrey Tsay). Mathematics and Computer Education, 39(2005), pp. 31-36. Download PDF File
57. Theon's ladder for any root (with Marcus Wright and Michael Orchard, International Journal of Mathematical Education in Science and Technology, 36(2005), pp. 389-398. Download PDF file
58. Why sin 80x looks like sin x on my TI-89, (with Jim Zeng).International Journal of Mathematical Education in Science and Technology, 36(2005), pp. 437-441. Download PDF file
59. Unexpected constructable numbers, The AMATYC Review, 26(2005), no. 2, pp. 2-3. Download PDF file
60. Some unusual expressions for the inradius of a triangle, (with Tirupathi R. Chandrupatla), The AMATYC Review, 26(2005), no.2, pp. 12-17. Download PDF file
61. A simple geometric construction of the harmonic mean of n variables (with Jim Zeng), Mathematical Spectrum, 37(2004/2005), No. 3, pp. 109-111. Download PDF file
62. Proof Without Words: Arc length of the cycloid, The Mathematical Gazette, 89(2005), no. 515, page 250. Download PDF file.
63. Ptolmey vs. Copernicus. (With Joseph Diaco.) The Mathematical Spectrum, 38(2005/2006), pp. 3-6. Download PDF File
64. The general Vieta-Wallis product for pi, The Mathematical Gazette, 89(2005), pp. 371-378. Download PDF File
65. Using simple harmonic motion to help in the search for tautochrone curves, (with Tirupathi R. Chandrupatia), International Journal of Mathematical Education in Science and Technology, 37 ( 2006), pp, 104-9. Download PDF file
66. Motivation for finding Zeta(2p) from a product of sines, International Journal of Mathematical Education in Science and Technology 37(2006), pp. 231-235. Download PDF file
67. A proof of the continued fraction for e^1/M, American Mathematical Monthly, 113(2006), pp. 62-66. Download PDF file
68. A mechanical view of Archimedes quadrature of the parabola. The College Mathematics Journal, 37(2006), pp. 24-28. Download PDF file
69. Interesting finite and infinite products from simple algebraic identities. The Mathematical Gazette, 90(2006), pp. 90-93. Download PDF File.
70 Proof with few
words: Quadratic convergence of the AGM, to appear in The Mathematical
Gazette 90(2006), pp. 116-117. Download
PDF File.
71. A spiral of triangles related to the great pyramid, with Matthew
Oster. The Mathematical Spectrum 38(2005/2006), pp. 108-112,.
Download
PDF File
72. An asymptotic approach to constructing the hyperbola,
with David Grochowski. The Mathematical
Spectrum 38(2005/2006), pp. 113-115. Download PDF File
73.. A collection of numbers
whose proof of irrationality is like that of the number e, (with Nicholas
Stugard). Mathematics and Computer Eduation,
40(2006), pp. 103-107. Download
PDF file
74. Translation with Notes of Euler's paper "Remarks on a beautiful relation between direct as well as reciprocal series" (E352),(with Lucas Willis), on the web at the Euler Archive, http://www.math.dartmouth.edu/~euler/. Download PDF FIle
75. Synopsis of Euler's paper "Remarks on a beautiful relation between direct as well as reciprocal series" (E352),(with Lucas Willis), on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/. Download PDF file
76. Translation with notes of Euler’s paper E796 (
with Kristen McKeen),
Recherches sur le
problem de trois nombres carres tels que
la somme de deux quelconques moins le troisieme fasse un nombre carre,“Research into
the problem of three square numbers such that the sum of any two less the third
one provides a square number.”, on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/.
Download
PDF file .
77. Synopsis by section of Euler's paper E769 ( with Kristen McKeen), Recherches sur le problem de trois nombres carres
tels que la somme de deux quelconques
moins le troisieme fasse un nombre carre,“Research into the problem of three square numbers
such that the sum of any two less the third one provides a square number”,
on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/.
Download PDF
file
78. Translation with notes of Euler's paper E46, Methodus
Universalis Serierum Convergentium Summas Quam Proxime Inveniendi, (A general
method for finding approximations to the sums of convergent series). (with Walter Jacob.) On the web at the
Euler Archive http://www.math.dartmouth.edu/~euler/. Download PDF
file
79. Synopsis of Euler's paper E46, Methodus
Universalis Serierum Convergentium Summas Quam Proxime Inveniendi, (A general
method for finding approximations to the sums of convergent series). (with Walter Jacob.) on the web at
the Euler Archive http://www.math.dartmouth.edu/~euler/. Download PDF file
80. The integers of James Booth, (with John F.
Kennedy), Mathematical Spectrum, 39(2006/2007), pp. 71-72. Download PDF file
81. A simple geometric method of estimating the error in
using Vieta's product for pi, International
Journal of Mathematics Education in Science and Technology, (38)2007, pp.
136-142. Download
PDF file
82. Some cosine relations and the regular heptagon, (
with Phongthong Heng)
Mathematics and Computer Education, (41)2007, pp. 17-21. Download PDF
file
83. Developing formulas by skipping rows in Pascal's
triangle (with Robert J. Buonpastore). Mathematics and Computer
Education, (41)2007, pp. 25-29. Download PDF
file
84. Some long telescoping series. The Mathematical Gazette, 91(2007),
pp. 104-5. Download
PDF file
85. Finding Zeta(2n) from a recursion
relation for Bernoulli numbers (with Jim Zeng), The Mathematical Gazette,
91(2007), pp. 123-6. Download PDF
file
86. The quadratic equation as solved by Persian mathematicians of the
middle ages, (with Mohamed Teymour). Mathematical
Spectrum, 39(2006/2007), pp. 115-8. Download
PDF file
87. Lucky fractions: Where bad arithmetic gives correct results, Mathematics and Computer Education,
41(2007), pp.162-167.Download PDF file
88. Constructing a line segment whose length is equal to the measure of a
given angle, (with Walter Jacob, IV), International Journal of Mathemeatical Education in Science and Technology,
38(2007), pp. 529-230. Download
PDF file
89. The unlikely connection between partitons and divisors, (with Abdul Hassen and T. R.
Chandrupatla), The College Mathematics Journal, 38(2007), pp. 278-287. Download
PDF FIle
90. Oblique-angled diameters and the conic sections,
with Edward Greve. The Mathematical Spectrum, 40(2007/2008),
pp. 26-30.. Download
PDF File
91. Geometric constructions approximating pi. Mathematical Spectrum, 40(2007/2008), pp106-108. Download PDF File
92. Vieta-like products
of nested radicals with Fibonacci and Lucas numbers, Fibonacci
Quarterly, 45(2008), pp. 202-204. Download PDF
File
93. An unusual proof that Fm divides Fmn for Fibonacci numbers using
hyperbolic functions, (with Adam Hilburn). The
Mathematical Gazette, 91(2007), pp. 510-512. Download
PDF File
94. Another geometric vision of the hyperbola.
Mathematical Spectrum
41(2008/2009). Pp. 123-4.
. Download
PDF File
95. Approximating the path of a celestial body with a circular orbit
from two close observations, (with Joseph Palma), The Mathematical
Scientist, 33(2008), pp. 8-14. Download
PDF File
96. Euler's little summation formula and sums of powers, (with
Andrew Robertson). Mathematical Spectrum, 40(2006/2007), pp. 73-76. Download
PDF File
97. Euler's little summation formula and special values of the zeta function,
The Mathematical Gazette, 92(2008), pp. 295-299. Download
PDF File
98. Exact values of the hyperbolic functions,
Mathematics and Computer Education, 42(2008), pp. 58-59. Download PDF
File
99. Using Theon's ladder to find roots of
quadratic equations,
Mathematics and Computer
Education, 42(2008), pp. 23-27. Download
PDF File
100. Translation with notes of Euler's paper E83, (with Edward Greve)On some properties
of conic sections that are shared with infinitely many other curved
lines. on the
web at the Euler Archive http://www.math.dartmouth.edu/~euler/. Download
PDF File
102. Triangles and parallelograms of equal area inside the
ellipse, (with Robert Buonpastore).
Mathematical Spectrum. 41(2008/2009), pp.
23-26. Download
PDF FIle
103. On generalizations of Lambert’s series, (with Abdul Hassen), International Journal of Pure and Applied Mathematics, 43(2008), 465-484. Download PDF FIle
104. Visualizing Vandermonde's convolution on the extended Pascal's triangle, (with Tirupathi R. Chandrupatia). Mathematics and Computer Education, 42(2008), pp. 118-122. Download PDF File
105. A remarkable formula for approximating the sum of alternating series. The Mathematical Gazette, 93(2009), pp.76-82. Download PDF FIle
106. Approximating an ellipse with four circular arcs, (with Tirupathi R. Chandrupatia), Mathematics and Computer Education, 42(2008), pp. 220-228. Download PDF File
107. More exact values of the hyperbolic functions, Mathematics and Computer Education, 42(2008), pp. 193-197. Download PDF File
108. A modern look at a neglected summation formula by Euler, (with Walter Jacob). The Mathematical Gazette, 93(2009), pp. 237-243. Download PDF file
109. Vieta-like products of nested radicals, The Mathematical Gazette, 94(2010), pp. 62-66. Download PDF File
110. On numbers equal to the sum of two squares in more than one way, (with Ming-Sun Li, Kathryn Robertson, Abdul Hassen, Christopher S. Simons and Marcus Wright). Mathematics and Computer Education, 43(2009), pp. 102-108. Download PDF File
111. Conjectures from a historic table by John Wallis, with Lee Collins. Mathematical Spectrum, 42(2009/2010), pp. 14-19. Download PDF File
112. Triangles of equal area in a hyperbola, with Adam Romasko, Mathematical Spectrum, 42(2009/2010), pp. 70-74. Download PDF File
113. Euler and the functional equation for the zeta function.The Mathematical Scientist. 34( 2009), pp. 62-73. Download PDF File
114 The tables of John Wallis and the discovery of his product for pi. The Mathematical Gazette, 94(2010), pp. 430-437. Download PDF file
115. Five historic formulas for pi. Mathematics and Computer Education, 43(2009), pp. 250-258. Download PDF File
116. Morphing Lord Brouncker’s
Continued Fraction for pi into the Product of Wallis. The Mathematical Gazette 95(2011), pp. 17-22.
Download PDF
file
117. Lord Brouncker’s forgotten sequence of continued fractions for pi. International Journal of Mathematical Education in Science and Technology, Volume 41, Issue 1 January 2010 , pages 105 – 110. Download PDF File
118. Translation with notes of Euler's paper E745, (with Christopher Tippie and Kristin Masters) On the continued fractions of Wallis. on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/. Download PDF FIle
119. Reflections and Notes on Euler’s paper E745, (with Christopher Tippie and Kristin Masters) On the continued fractions of Wallis. on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/. Download PDF File
120. Synopsis of Euler’s paper E745, (with Christopher Tippie and Kristin Masters) On the continued fractions of Wallis. on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/. Download PDF File
121. . Euler’s parallel oblique angled diameters, The Mathematical Gazette,
95(2011), pp. 40-48. Download
PDF file
122. Translation of Euler's paper , (with Jasen Scaramazza) Memoire sur la plus grande equation des planets, (Memoir on the Maximum value of an Equation of the Planets). on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/. Download PDF file
123. Notes on Euler's paper , (with Jasen Scaramazza) Memoire sur la plus grande equation des planets, (Memoir on the Maximum value of an Equation of the Planets). on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/. Download PDF file
124. Synopsis of Euler's paper , (with Jasen Scaramazza) Memoire sur la plus grande equation des planets, (Memoir on the Maximum value of an Equation of the Planets). on the web at the Euler Archive http://www.math.dartmouth.edu/~euler/. Download PDF file
125 The perimeter of an ellipse, (with Tirupathi R. Chandrupatla).The Mathematical Scientist, 35 (2010), pp. 122-131. Download PDF file
126. An interesting generalization of the half angle formulas to complex numbers, (with Marcus Wright), The Mathematical Gazette, 95(2011), p. 327. Download PDF file
127. Euler’s method of integration by parts (with Steve Donahue),
The Mathematical Gazette. 96(2012), pp.
115-116. Download
PDF file
128. Planar biarc curves – A geometric view, (with T. R. Chandrupatla). The Mathematical Scientist. 36(2011), pp. 126-132. Download PDF file
129. Law of cosines
generalized for any polygon and any polyhedron, (with Lee Collins), The
Mathematical Gazette, 95(2011), pp. 240-243. Download
PDF file
130. The missing fractions in Brouncker’s sequence of continued fractions for pi. The Mathematical Gazette, 96(2012), pp. 221-225. Download PDF file
131. How Euler found the eccentricity of planetary orbits, (with Jasen Scaramazza). Accepted on November 28, 2011 by The Mathematical Scientist. To appear December, 2012. Download PDF file
132. Diophantine approximation and the irrationality of certain numbers, (with Eric Jones). Mathematics and Computer Education, 46(2012), pp. 125 - 130. Download PDF file
133. Partial sums of divergent series that cannot be an integer. Accepted on January 24, 2012. Due to appear November 2012 in the Mathematical Gazette.
134. The devil’s series – Did it fool Euler. (with Steven Donahue), The Mathematical Gazette, 97(2013), pp. 133 – 137.
135. An interesting bilateral series generalizing the series for zeta of 2, (with Cory Wright), The Mathematical Gazette, 97(2013), pp. 131 – 133.
136. Unexpected connections between three famous formulas for pi. Submitted via email to the Mathematical Scientist on March 25, 2012. Accepted on April 13,
137. Four derivations of an interesting bilateral series generalizing the
series for zeta of 2. (with Cory Wright). The
International Journal of Mathematical Education in Science and Technology,
44(2013), pp. 456 – 461.
138. Interesting subseries of the harmonic series. Mathematics and Computer Education, 46(2012),
pp. 169 – 173.