Logarithmic integral function information

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...

a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. Note: x >...

(elliptic integral) 1 ln ⁡ x {\displaystyle {\frac {1}{\ln x}}} (logarithmic integral) e − x 2 {\displaystyle e^{-x^{2}}} (error function, Gaussian integral) sin...

mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an...

mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle {\frac {f'}{f}}}...

of x. A far better estimate of π(x) is given by the offset logarithmic integral function Li(x), defined by L i ( x ) = ∫ 2 x 1 ln ⁡ ( t ) d t . {\displaystyle...

trigonometric functions were often combined with logarithms in compound functions like the logarithmic sine, logarithmic cosine, logarithmic secant, logarithmic cosecant...

\Re (z)>0\,.} The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in...

mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions are Si...

below are negative. Integrals also refer to the concept of an antiderivative, a function whose derivative is the given function; in this case, they are...

function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function...

the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and...

logarithmic identities Logarithm of a matrix Logarithmic coordinates of an element of a Lie group. Logarithmic differentiation Logarithmic integral function...

Liouville function, λ(n) = (–1)Ω(n) Von Mangoldt function, Λ(n) = log p if n is a positive power of the prime p Carmichael function Logarithmic integral function:...

functions List of integrals of exponential functions List of integrals of logarithmic functions List of integrals of Gaussian functions Gradshteyn, Ryzhik...

multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables...

polylogarithmic functions, nor with the offset logarithmic integral Li(z), which has the same notation without the subscript. Different polylogarithm functions in...

function li occurring in the first term is the (unoffset) logarithmic integral function given by the Cauchy principal value of the divergent integral...

list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals. Indefinite integrals are antiderivative...

calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative...

elementary but lack elementary antiderivatives; the integral of the Gaussian function is the error function: ∫ e − x 2 d x = π 2 erf ⁡ x + C . {\displaystyle...

Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral li(x) (under the slightly different form of a series, which...

"logarithmic" to "logistic" transition first noted by Pierre-François Verhulst, as noted above) and then reaching a maximal limit. A logistic function...

Thailand Long Island, New York Li, the polylogarithm function Li, the logarithmic integral function <li></li>, indicating an item in an HTML list; see HTML...

direct integration of a complex-valued function along a curve in the complex plane; application of the Cauchy integral formula; and application of the residue...

what would now be called an integration of this function, where the formulae for the sums of integral squares and fourth powers allowed him to calculate...