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Higher Transcendental Functions - Volume I - Based, in part, on notes left by Harry Bateman (PDF). Bateman Manuscript Project. Vol. I (1 ed.). New York / Toronto / London: McGraw-Hill Book Company, Inc. LCCN 53-5555. Contract No. N6onr-244 Task Order XIV. Project Designation Number: NR 043-045. Order No. 19545.
An example is the function that relates each real number x to its square x 2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. The input variable(s) are sometimes referred to as the argument(s) of the function.
A differential equation is an equation involving an unknown function and its derivatives. In a dynamical system , a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are ...
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
Michael Danos and Johann Rafelski edited the Pocketbook of Mathematical Functions, published by Verlag Harri Deutsch in 1984. [14] [15] The book is an abridged version of Abramowitz's and Stegun's Handbook, retaining most of the formulas (except for the first and the two last original chapters, which were dropped), but reducing the numerical tables to a minimum, [14] which, by this time, could ...
According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews (MR) database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The ...
[12] [10] [13] [11] Repeated composition of such a function with itself is called function iteration. By convention, f 0 is defined as the identity map on f 's domain, id X . If Y = X and f : X → X admits an inverse function f −1 , negative functional powers f − n are defined for n > 0 as the negated power of the inverse function: f − n ...
A related function counts prime powers with weight 1 for primes, 1/2 for their squares, 1/3 for cubes, etc. It is the summation function of the arithmetic function which takes the value 1/k on integers which are the kth power of some prime number, and the value 0 on other integers.