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For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power. The word "raised" is usually omitted, and sometimes "power" as well, so 3 5 can be simply read "3 to the 5th", or "3 to
For each integer n > 2, the function n x is defined and increasing for x ≥ 1, and n 1 = 1, so that the n th super-root of x, , exists for x ≥ 1. One of the simpler and faster formulas for a third-degree super-root is the recursive formula, if: x x x = a , and next x ( n + 1) = exp (W (W ( x ( n ) ln ( a )))) , for example x (0) = 1 .
Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
Power series. In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the n th term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions.
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. Powers of two with non-negative exponents are integers: 20 = 1, 21 = 2, and 2n is two multiplied by itself n times. [1][2] The first ten powers of 2 for non-negative values of n are:
A formal power series can be loosely thought of as an object that is like a polynomial, but with infinitely many terms.Alternatively, for those familiar with power series (or Taylor series), one may think of a formal power series as a power series in which we ignore questions of convergence by not assuming that the variable X denotes any numerical value (not even an unknown value).
Indeterminate form. In calculus, it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function. For example, and likewise for other arithmetic operations; this is sometimes called the algebraic limit theorem.
This formula can be used to compute () with floating point operations for real between 0 and 2.5. For x > 2.5 {\displaystyle x>2.5} , the result is inaccurate due to cancellation . A faster converging series was found by Ramanujan :