Special functions | Analytic functions
In mathematics, the Mittag-Leffler function is a special function, a complex function which depends on two complex parameters and . It may be defined by the following series when the real part of is strictly positive: where is the gamma function. When , it is abbreviated as .For , the series above equals the Taylor expansion of the geometric series and consequently . In the case and are real and positive, the series converges for all values of the argument , so the Mittag-Leffler function is an entire function. This function is named after Gösta Mittag-Leffler. This class of functions are important in the theory of the fractional calculus. For , the Mittag-Leffler function is an entire function of order , and is in some sense the simplest entire function of its order. The Mittag-Leffler function satisfies the recurrence property (Theorem 5.1 of ) from which the Poincaré asymptotic expansion follows, which is true for . (Wikipedia).
Free ebook http://tinyurl.com/EngMathYT A lecture discussing Lagrange multipliers: the method and why it works. Plenty of examples are presented to illustrate the ideas.
From playlist Lagrange multipliers
When do fractional differential equations have solutions bounded by the Mittag-Leffler function?
When do fractional differential equations have solutions bounded by the Mittag Leffler function? New research into this question! http://www.degruyter.com/view/j/fca.2015.18.issue-3/fca-2015-0039/fca-2015-0039.xml?format=INT Fract. Calc. Appl. Anal. 18, no. 3 (2015), 642-650. DOI: 10.15
From playlist Mathematical analysis and applications
Loose the screw for moving the stopper to new position and then tighten it. The stopper is kept immobile by wedge mechnism.
From playlist Mechanisms
Lagrange multipliers: 2 constraints
Free ebook http://tinyurl.com/EngMathYT A lecture showing how to apply the method of Lagrange multipliers where two contraints are involved.
From playlist Lagrange multipliers
Banach fixed point theorem & differential equations
A novel application of Banach's fixed point theorem to fractional differential equations of arbitrary order. The idea involves a new metric based on the Mittag-Leffler function. The technique is applied to gain the existence and uniqueness of solutions to initial value problems. http://
From playlist Mathematical analysis and applications
Gronwall's inequality & fractional differential equations
Several general versions of Gronwall's inequality are presented and applied to fractional differential equations of arbitrary order. Applications include: yielding a priori bounds and nonumultiplicity of solutions. This presentation features new mathematical research. http://projecteucli
From playlist Mathematical analysis and applications
This lecture is part of an online course on rings and modules. We discuss when taking limits of modules preserves exactness. In particular we give the Mittag-Leffler condition that ensures that taking inverse limits of modules preserves exactness. For the other lectures in the course see
From playlist Rings and modules
The Cotangent's Series Expansion Derivation using FOURIER SERIES [ Mittag-Leffler Theorem ]
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From playlist Fourier Series
Lagrange Multipliers - Two Constraints
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Lagrange Multipliers - Two Constraints. In this video, I show how to find the maximum and minimum value of a function subject to TWO constraints using Lagrang
From playlist All Videos - Part 8
Commutative algebra 48: Limits and exactness
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss when the limit of exact sequences is exact. We show this happens whenever the "Mittag-Leffler condition" is satisfi
From playlist Commutative algebra
15.5: Lagrange Multipliers Example - Valuable Vector Calculus
Explanation of Lagrange multipliers: https://youtu.be/bmTiH4s_mYs An example of the actual problem-solving techniques to find maximum and minimum values of a function with a constraint using Lagrange multipliers. Full Valuable Vector Calculus playlist: https://www.youtube.com/playlist?li
From playlist Valuable Vector Calculus
Hermitian and Non-Hermitian Laplacians and Wave Equaions by Andrey shafarevich
Non-Hermitian Physics - PHHQP XVIII DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Phys
From playlist Non-Hermitian Physics - PHHQP XVIII
homemade lathe taper attachment. probably beefier than it needs to be, but made of materials on-hand.
From playlist Tips, Tricks, and Techniques
Lennart Carleson - The Abel Prize interview 2006
0:00 Glimpses of the Abel Prize ceremony made for Norwegian television 05:00 Interview proper starts (Norwegian) 07:46 (English) Almost-everywhere convergence of Fourier series for square-integrable (L^2) functions 10:08 Interesting example of need to have conviction about outcome before c
From playlist The Abel Prize Interviews
Background material on the Cauchy-Riemann equations (Lecture 1) by Debraj Chakrabarti
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - David Rowe - 17/11/17
En partenariat avec le séminaire d’histoire des mathématiques de l’IHP Wartime Memories of Gaston Darboux in Göttingen David Rowe, Université de Mayence, Allemagne À l’occasion du centenaire de la mort de Gaston Darboux, l’Institut Henri Poincaré souhaite retracer la figure du géomètre s
From playlist Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - 17/11/2017