MATHEMATICAL
PUBLICATIONS
May 21, 2008
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 related to Vieta's product of nested radicals. To appear in The Mathematical Spectrum. Download PDF File
92. Vieta-like products of nested radicals with Fibonacci
and Lucas numbers. To appear in the Fibonacci Quarterly. 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. To appear in The Mathematical
Spectrum. Download
PDF File
95. Approximating the path of a celestial body with a circular orbit
from two close observations, (with Joseph Palma) To appear in The
Mathematical Scientist. Download
PDF File
96. Euler's little summation formula and sums of powers, (with Andrew
Robertson). To appear in The Mathematical Spectrum. Download
PDF File
97. Euler's little summation formula and special values of the zeta function.
To appear in The Mathematical Gazette in July 2008. Download
PDF File
98. Exact values of the hyperbolic functions. Submitted to Mathematics
and Computer Education on January 3, 2007 via email. Accepted August, 2007. Download PDF
File
99. Using Theon's ladder to find roots of quadratic equations. Submitted
to Mathematics and Computer Education on January 4, 2007 via email. Accepted
August 20, 2007. 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. To appear on the Euler Archive. Download
PDF File
102. Triangles and parallelograms of equal area inside the ellipse,
(with Robert Buonpastore). To appear in The Mathematical Spectrum. 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.
105. A remarkable formula for approximating the sum of alternating series. To appear in The Mathematical Gazette in March, 2009.
106. Approximating an ellipse with four circular arcs, (with Tirupathi R. Chandrupatia). To appear in Mathematics and Computer.
107. More exact values of the hyperbolic functions. To
appear in Mathematics and Computer Education.