Mathematical Constants

by Steven R. Finch

Clay Mathematics Institute Book Fellow

My website is smaller than it once was. Please visit again, however, since new materials will continue to appear occasionally. *

My book Mathematical Constants is now available for online purchase from Cambridge University Press (in the United Kingdom, North America and Australia). It is far more encompassing and detailed than my website ever was. It is also lovingly edited and beautifully produced - many thanks to Cambridge! - please support us in our publishing venture. Thank you. (If you wish, see several very kind reviews. You can also search the book via Amazon and Google by keyword.)

Here are errata and addenda to the book (last updated 9/2/2009), as well sample essays from the book about integer compositions, optimal stopping and Reuleaux triangles. Here also are recent supplementary materials, organized by topic:

Number Theory and Combinatorics

Bipartite, k-colorable and k-colored graphs (6/5/2003)
Transitive relations, topologies and partial orders (6/5/2003)
Series-parallel networks (7/7/2003)
Two asymptotic series (12/10/2003)
Multiples and divisors (1/27/2004)
Discrepancy and uniformity (2/19/2004)
Unitarism and infinitarism (2/25/2004)
Erdös' minimum overlap problem (7/2/2004)
Planar graph growth constants (8/25/2004)
Tauberian constants (8/30/2004)
Integer partitions (9/22/2004)
Class number theory (5/26/2005)
Quadratic Dirichlet L-series (7/15/2005)
Elliptic curves over Q (10/10/2005)
Modular forms on SL₂(Z) (12/28/2005)
Chebyshev's bias (4/26/2006)
Pattern-avoiding permutations (4/27/2006)
Cyclic group orders (4/28/2006)
Dedekind eta products (1/10/2007)
Series involving arithmetic functions (1/24/2007)
Riemann zeta moments (3/22/2007)
Central binomial coefficients (3/28/2007)
Fractional parts of Bernoulli numbers (4/10/2007)
Products of consecutive-integer ratios (4/19/2007)
Prime number theorem (4/27/2007)
Mertens' formula (5/4/2007)
Cyclotomic polynomials (3/31/2008)
Minkowski-Alkauskas constant (5/6/2008)
Two-colorings of positive integers (5/27/2008)
Signum equations and extremal coefficients (2/7/2009)
Monoids of natural numbers (3/17/2009)
Primitive cusp forms (4/27/2009)
Cubic and quartic characters (6/5/2009)
Distribution of error terms (9/9/2009)

Inequalities and Approximation

Hardy-Littlewood maximal inequalities (10/12/2003)
Bessel function zeroes (10/23/2003)
Nash's inequality (11/4/2003)
Uncertainty inequalities (11/7/2003)
Airy function zeroes (7/19/2004)
Projections of minimal norm (11/30/2004)
Bohr's inequality (12/5/2004)
Moduli of continuity (12/22/2004)
Quinn-Rand-Strogatz constant (4/27/2008)
Tsirelson's constant (8/19/2008)
Mathieu eigenvalues (10/7/2008)
Thomas-Fermi model (10/15/2008)
Prandtl-Blasius flow (11/12/2008)
Lane-Ritter-Emden constants (11/30/2008)
Brachistochrone problem (12/17/2008)
Radiative transfer equations (12/30/2008)

Real and Complex Analysis

Radii in geometric function theory (1/5/2004)
Numerical radii of linear operators (4/5/2005)
Coefficient estimates for univalent functions (12/15/2004)
Planar harmonic mappings (3/29/2005)
Constant of interpolation (4/5/2005)
Dirichlet integral (5/15/2008)
Dyadic UMD constants (3/24/2009)

Probability and Stochastic Processes

Hammersley's path process (4/5/2004)
Moments of sums (4/23/2004)
Ornstein-Uhlenbeck process (5/15/2004)
Zero crossings (5/19/2004)
Variants of Brownian motion (6/12/2004)
Shapes of binary trees (6/24/2004)
Expected lifetimes and inradii (2/23/2005)
Subcritical Galton-Watson trees (3/1/2007)
Continued fraction transformation (5/23/2007)
Continued fraction transformation. II (6/15/2007)
Continued fraction transformation. III (7/1/2007)
Continued fraction transformation. IV (7/18/2007)
Lyapunov exponents (11/19/2007)
Lyapunov exponents. II (11/20/2007)
Lyapunov exponents. III (11/21/2007)
Lyapunov exponents. IV (3/18/2008)
Stars and watermelons (4/26/2008)
Prophet inequalities (5/9/2008)
Excursion durations (5/12/2008)
Gambler's ruin (6/19/2008)
Self-convolutions (3/2/2009)

Geometry and Topology

Knots, links and tangles (8/8/2003)
Convex lattice polygons (12/18/2003)
Volumes of hyperbolic 3-manifolds (9/5/2004)
Poisson-Voronoi tessellations (3/11/2005)
Optimal escape paths (5/30/2005)
Minkowski-Siegel mass constants (1/9/2005)
Slicing problem (4/5/2005)
Constant of Theodorus (4/9/2005)
Nearest-neighbor graphs (4/25/2008)

Here are several favorite links: Mathematical Constants and Computation (by X. Gourdon and P. Sebah), MathWorld Constants (by E. Weisstein at Wolfram Research), the Inverse Symbolic Calculator (by S. Plouffe), and the On-Line Encyclopedia of Integer Sequences (by N. Sloane).

Here finally is contact information for me. I appreciate your interest!

* In October 2002, a former employer demanded that this website be shut down, and I had no choice but to comply (draft notes here & here). I am grateful to Cambridge University Press and to INRIA Rocquencourt for patiently seeing me through a difficult time (up to June 2003).