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 >...

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

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...

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}}}...

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

mathematical constant defined as the unique positive zero of the logarithmic integral function. It is named after Srinivasa Ramanujan and Johann Georg von...

The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic...

derivative, primitive function, primitive integral or indefinite integral of a continuous function f is a differentiable function F whose derivative is...

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...

\pi } denotes the prime counting function, Li {\displaystyle \operatorname {Li} } the logarithmic integral function with inverse Li − 1 {\displaystyle...

\left(x^{1/n}\right),} μ(n) is the Möbius function, li(x) is the logarithmic integral function, ρ indexes every zero of the Riemann zeta function, and li(x⁠ρ/n⁠) is not...

particularly in relation to the evaluation of many classes of logarithmic and polylogarithmic integrals, both definite and indefinite. They also have numerous...

List of integrals of exponential functions List of integrals of logarithmic functions List of integrals of area functions Partial derivative Disk integration...

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

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

{\displaystyle x} for which the prime-counting function π ( x ) {\displaystyle \pi (x)} exceeds the logarithmic integral function li ⁡ ( x ) . {\displaystyle \operatorname...

as the sine integral, an antiderivative of the sinc function, is not an elementary function. In this case, the improper definite integral can be determined...

\psi (z)} is the digamma function, the logarithmic derivative of the gamma function. There is also a corresponding integral formula (for Re(x) > 0): Y...

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:...

In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln ⁡ Γ ( z ) = Γ ′ ( z ) Γ ( z )...

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...

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

offset logarithmic integral function. li – logarithmic integral function or linearly independent. lim – limit of a sequence, or of a function. lim inf...

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

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...

The term integral logarithm may stand for: Discrete logarithm in algebra, Logarithmic integral function in calculus. This disambiguation page lists articles...

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

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