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A Riemann

**sum**of a function f with respect to such a tagged partition is defined as ∑ i = 1 n f ( t i ) Δ i ; {\displaystyle \**sum**_{i=1}^{n}f(t_{i})\,\Delta _{i};} thus each term of the**sum**is the area of a rectangle with height equal to the function value at the distinguished point of the given sub-interval, and width the same as the width ...Elementary rules of

**differentiation**. Unless otherwise stated, all functions are functions of real numbers that return real values; although more generally, the formulae below apply wherever they are well defined — including the case of complex numbers ().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.A geometric series is the

**sum**of the numbers in a**geometric progression**. For example: + + + = + + +. Letting a be the first term (here 2), n be the number of terms (here 4), and r be the constant that each term is multiplied by to get the next term (here 5), the**sum**is given by:Hyperbolic tangent. The hyperbolic tangent is the (unique) solution to the differential equation f ′ = 1 − f 2, with f (0) = 0.. Useful relations. The hyperbolic functions satisfy many identities, all of them similar in form to the trigonometric identities.

**Market value**or OMV (Open Market Valuation) is the price at which an asset would trade in a competitive auction setting.**Market value**is often used interchangeably with open**market value**, fair value or fair**market value**, although these terms have distinct definitions in different standards, and differ in some circumstances.Ratios are also problematic; normal approximations exist under certain conditions. Example formulae. This table shows the variances and standard deviations of simple functions of the real variables ,, with standard deviations ,, covariance =, and correlation .

In waveform combinations. Waveforms made by summing known simple waveforms have an RMS value that is the root of the

**sum**of squares of the component RMS values, if the component waveforms are orthogonal (that is, if the average of the product of one simple waveform with another is zero for all pairs other than a waveform times itself).