Concepts inComputing multivariable Taylor series to arbitrary order
Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. The concept of a Taylor series was formally introduced by the English mathematician Brook Taylor in 1715.
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Multivariable calculus
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus in more than one variable: the differentiated and integrated functions involve multiple variables, rather than just one.
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Binomial coefficient
In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written, and it is the coefficient of the x term in the polynomial expansion of the binomial power (1 + x). Arranging binomial coefficients into rows for successive values of n, and in which k ranges from 0 to n, gives a triangular array called Pascal's triangle.
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Elementary function
In mathematics, an elementary function is a function of one variable built from a finite number of exponentials, logarithms, constants, and nth roots through composition and combinations using the four elementary operations (+ ¿ × ÷). By allowing these functions (and constants) to be complex numbers, trigonometric functions and their inverses become included in the elementary functions.
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Automatic differentiation
In mathematics and computer algebra, automatic differentiation (AD), sometimes alternatively called algorithmic differentiation, is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc. ) and elementary functions (exp, log, sin, cos, etc.).
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APL (programming language)
APL (named after the book A Programming Language) is an interactive array-oriented language and integrated development environment, which is available from a number of commercial and noncommercial vendors and for most computer platforms. It is based on a mathematical notation developed by Kenneth E. Iverson and associates that features special attributes for the design and specifications of digital computing systems, both computer hardware and software.
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Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.
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