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More detail may be found on the following pages for the lists of integrals : Gradshteyn, Ryzhik, Geronimus, Tseytlin, Jeffrey, Zwillinger, and Moll 's (GR) Table of Integrals, Series, and Products contains a large collection of results. An even larger, multivolume table is the Integrals and Series by Prudnikov, Brychkov, and Marichev (with ...
Toyesh Prakash Sharma, Etisha Sharma, "Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.1-8, 2023.
Square-integrable function. In mathematics, a square-integrable function, also called a quadratically integrable function or function or square-summable function, [1] is a real - or complex -valued measurable function for which the integral of the square of the absolute value is finite. Thus, square-integrability on the real line is defined as ...
The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function over the entire real line. Named after the German mathematician Carl Friedrich Gauss, the integral is. Abraham de Moivre originally discovered this type of integral in 1733, while Gauss published the precise integral in 1809. [1]
Definition and divergence. The harmonic series is the infinite series in which the terms are all of the positive unit fractions. It is a divergent series: as more terms of the series are included in partial sums of the series, the values of these partial sums grow arbitrarily large, beyond any finite limit.
The integral of the secant function was historically one of the first integrals of its type ever evaluated, before most of the development of integral calculus. It is important because it is the vertical coordinate of the Mercator projection, used for marine navigation with constant compass bearing .
The graph forms a rectangular hyperbola. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/ x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a / b is b / a. For the multiplicative inverse of a real number, divide 1 by the number.
For the special antiderivatives involving trigonometric functions, see Trigonometric integral. [ 1] Generally, if the function is any trigonometric function, and is its derivative, {\displaystyle \int a\cos nx\,dx= {\frac {a} {n}}\sin nx+C} In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration .