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The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4. The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1. The minimum value of x is ...
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
Rather, the above product representation of ζ(z) converges precisely for Re(z) > 1, where it is an analytic function. By techniques of analytic continuation, this function can be extended uniquely to an analytic function (still denoted ζ(z)) on the whole complex plane except at the point z = 1, where it has a simple pole.
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By using the product rule, one gets the derivative ′ = + (since the derivative of is , and the derivative of the sine function is the cosine function). One special case of the product rule is the constant multiple rule, which states: if c is a number, and () is a differentiable function, then () is also differentiable, and its derivative is
Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. 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.
Mathematics portal; John Wallis, English mathematician who is given partial credit for the development of infinitesimal calculus and pi. Viète's formula, a different infinite product formula for . Leibniz formula for π, an infinite sum that can be converted into an infinite Euler product for π. Wallis sieve
If f is a function from X to A and g is a function from Y to B, then their Cartesian product f × g is a function from X × Y to A × B with (,) = ((), ()). This can be extended to tuples and infinite collections of functions. This is different from the standard Cartesian product of functions considered as sets.