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Everything about Logarithmic integral function
Special function defined by an integral
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 less than or equal to a given value x. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Logarithmic integral functionA 5-minute orientation
- Skim a recent paper: Piecewise logarithmic Chebyshev cardinal functions: Application for nonlinear integral equations with a logarithmic singular kernelInfluential work since 2022
- Pick up a classic book: The logarithmic integralThe most-reprinted book on the subject
- Read the landmark paper: Integral representations and properties of some functions involving the logarithmic functionCited 16 times
- Go sideways: Exponential integralA closely related topic
- Go sideways: Digamma functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Integral representations and properties of some functions involving the logarithmic function
Integral logarithmic means for regular functions
A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function
An Integral Representation of the Logarithmic Function with Applications in Information Theory
Integral definition of the logarithmic function and the derivative of the exponential function in calculus
DEFINITE INTEGRAL OF LOGARITHMIC FUNCTIONS AND POWERS IN TERMS OF THE LERCH FUNCTION
Definite Integral of Logarithmic Power and Square Root Algebraic Functions Expressed in terms of the Lerch Function
Pathway fractional integral representations for extended hypergeometric logarithmic functions
🆕 Influential since 2022
Piecewise logarithmic Chebyshev cardinal functions: Application for nonlinear integral equations with a logarithmic singular kernel
Integral representations with logarithmic and certain special functions
Triple Integral involving the Product of the Logarithmic and Bessel Functions expressed in terms of the Lerch Function
j-Dimensional Integral Involving the Logarithmic and Exponential Functions: Derivation and Evaluation
Sharp fractional integral inequalities for generalized logarithmic Godunova-Levin functions via Riemann-Liouville operators
📚 Books worth reading
The logarithmic integralPaul Koosis · 1988- 📕Magnitudinum exponentialium logarithmorum et trigonometriae sublimis theoriaPietro Ferroni · 1782
Low-voltage CMOS log companding analog designFrancisco Serra-Graells · 2003
The Logarithmic Integral (Cambridge Studies in Advanced Mathematics)Paul Koosis · 1992
Low-voltage CMOS log companding analog design · 2003
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Gamma function This article uses technical mathematical notation for logarithms. All instances of log(x) without a subscript base should be interpreted as a natural…
- List of logarithmic identities In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes…
- Prime-counting function This article uses technical mathematical notation for logarithms. All instances of log(x) without a subscript base should be interpreted as a natural…
- Stirling's approximation In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to…