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power, in the formula The Dirichlet inverse of Liouville function is the absolute value of the Möbius function, \lambda ^{-1}(n)=|\mu (n)|=\mu ^{2}(n), (\lambda...

the problem statement as given. If we denote the Sturm-Liouville operator by L, the Sturm-Liouville problem is Lu = w(x). What we want is to solve for u...

It would be nice to create a disambiguation page for Liouville equation. Currently the similarly-named equation from physics hogs up all the possible...

connection between zeros of Riemann zeta function and Liouville function sum? And why one zero of this function, with imaginary part a bit larger than 14...

from Liouville's theorem, as given in this article. In the introduction, they say, The distribution function is assumed to satisfy the Liouville equation...

following two concepts: Liouville's theorem which states that if an entire function f is bounded, then f is constant Trigonometric functions like sine and cosine...

suggest moving this to elementary function and deleting the disambiguation page. "an elementary function is a function built from a finite number of exponentials...

Green's function gives solutions to inhomogeneous differential-integral equations, most commonly a Sturm-Liouville problem. If G is the Green's function of...

your function it would be _always zero_. This is precisely the kind of thing generalized functions were invented for! 3. The phase space (Liouville) measure_is...

edu/viewdoc/download?doi=10.1.1.679.2560&rep=rep1&type=pdf The link attached to "Liouville measure" in the section "Concentration of measure in physics" leads to...

Riesz on Riemann-Liouville integrals (fractional calculus) from 1938, Bochner (1932) and Carleman (1944) on Fourier transforms of functions of polynomial...

I needed. The subject has its origins in Liouville's papers centered on a theorem (now known as Liouville's principle) that gives the form of an elementary...

singularities; - an elliptic function with no singularity is constant by Liouville's theorem. The usual construction of a Gw function is as a difference of Weierstrass...

tweaked and moved as a "Special case of basic power functions" section in the Riemann–Liouville_integral article. Same with the Laplace transform section...

was first introduced by Dirichlet and some other mathematician (perhaps Liouville). We should check the historical information ! —Preceding unsigned comment...

1682 paper where he proved sin x is not an algebraic function of x." And then: Joseph Liouville first proved the existence of transcendental numbers in...

20:48, 16 December 2020 (UTC) For historical reasons I think a section on Liouville numbers belongs in both articles. Pi and e I think fit best into the transcendental...

(l+1)=\lambda } 1) This has nothing to do with "Sturm-Liouville", the connection to "Sturm-Liouville" comes later in the analysis 2) Here one restricts oneself...

initialized (used) properly.) By far, the most common form is the Riemann-Liouville form: a D t q f ( x ) = 1 Γ ( n − q ) d n d x n ∫ a t ( t − τ ) n − q...

method that allows one to only consider a finite set of elementary functions of Liouville's form." Can anybody enlighten me on this? --Berntie (talk) 20:19...