Search results
Results from the WOW.Com Content Network
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number theoretic significance. In particular, according to the prime number theorem , it is a very good approximation to the prime-counting function , which is defined as the number of prime numbers ...
The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity.
The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see Lists of integrals.
The natural logarithm of t can be defined as the definite integral: =. This definition has the advantage that it does not rely on the exponential function or any trigonometric functions; the definition is in terms of an integral of a simple reciprocal.
Since sinc is an even entire function (holomorphic over the entire complex plane), Si is entire, odd, and the integral in its definition can be taken along any path connecting the endpoints. By definition, Si(x) is the antiderivative of sin x / x whose value is zero at x = 0, and si(x) is the antiderivative whose value is zero at x = ∞.
The principal value defines a particular complex logarithm function : that is continuous except along the negative real axis; on the complex plane with the negative real numbers and 0 removed, it is the analytic continuation of the (real) natural logarithm.
Although the main definition of the gamma function—the Euler integral of the second kind—is only valid (on the real axis) for positive arguments, its domain can be extended with analytic continuation [13] to negative arguments by shifting the negative argument to positive values by using either the Euler's reflection formula ...
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.