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Euler's number: 2.71828... 35 000 000 000 000 26 Dec 2023 Jordan Ranous Euler-Mascheroni constant: 0.57721... 1 337 000 000 000 7 Sep 2023 Andrew Sun Apéry constant: 1.20205... 2 020 569 031 595 22 December 2023 Andrew Sun Lemniscate constant: 2.62205... 1 200 000 000 100 15 July 2022 Seungmin Kim Catalan's constant: 0.91596... 1 200 000 000 ...
The Euler numbers are related to a special value of the Euler polynomials, namely: = (). The Euler numbers appear in the Taylor series expansions of the secant and hyperbolic secant functions. The latter is the function in the definition.
Variables of BigNumber type can be used, or regular numbers can be converted to big numbers using conversion operator # (e.g., #2.3^2000.1). SmartXML big numbers can have up to 100,000,000 decimal digits and up to 100,000,000 whole digits.
Hermes Project: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers. IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices. IT++ is a C++ library for linear algebra (matrices and vectors), signal processing and communications ...
Euler handles symbolic computations via Maxima, which is loaded as a separate process, communicating with Euler through pipes. The two programs can exchange variables and values. Indeed, Maxima is used in various Euler functions (e.g. Newton's method) to assist in the computation of derivatives, Taylor expansions and integrals. Moreover, Maxima ...
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
SU2 is a suite of open-source software tools written in C++ for the numerical solution of partial differential equations (PDE) and performing PDE-constrained optimization. The primary applications are computational fluid dynamics and aerodynamic shape optimization , [ 2 ] but has been extended to treat more general equations such as ...
Using the same approach, in 2013, M. Ram Murty and A. Zaytseva showed that the generalized Euler constants have the same property, [3] [44] [45] where the generalized Euler constant are defined as = (= = ()), where is a fixed list of prime numbers, () = if at least one of the primes in is a prime factor of , and ...