Alan Baker and Gisbert Wüstholz, Logarithmic Forms and Diophantine Geometry, New Mathematical Monographs 9, Cambridge University Press, 2007, ISBN 978-0-521-88268-2
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Cahen's constant, an infinite series of unit fractions, with alternating signs, derived from Sylvester's sequence
Simon Plouffe gives an infinite collection of identities between the trigamma function, π2 and Catalan's constant; these are expressible as paths on a graph.
where is the number of magnetic atoms (or molecules) per unit volume, is the Landé g-factor, (9.27400915e-24 J/T or A·m2) is the Bohr magneton, is the angular momentum quantum number and is Boltzmann's constant.
The Gelfond–Schneider theorem answers affirmatively Hilbert's seventh problem.
On the other hand, the Compton wavelength, , where h is Planck's constant, represents a limit on the minimum size of the region in which a mass M at rest can be localized.
where Q is a quantity that represents the amount of electricity present at each of the two points, and ke is Coulomb's constant.
Paul Davies and collaborators have suggested that it is in principle possible to disentangle which of the dimensionful constants (the elementary charge, Planck's constant, and the speed of light) of which the fine-structure constant is composed is responsible for the variation.