In mathematics, a Lidstone series, named after George James Lidstone, is a kind of polynomial expansion that can express certain types of entire functions. Let ƒ(z) be an entire function of exponential type less than (N + 1)π, as defined below. Then ƒ(z) can be expanded in terms of polynomials An as follows: Here An(z) is a polynomial in z of degree n, Ck a constant, and ƒ(n)(a) the nth derivative of ƒ at a. A function is said to be of exponential type of less than t if the function is bounded above by t. Thus, the constant N used in the summation above is given by with (Wikipedia).
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From playlist 80's
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From playlist Classical
Worldwide Calculus: Theorems on Series III: Series with Positive and Negative Terms
Lecture on 'Theorems on Series III: Series with Positive and Negative Terms' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Direct Comparison Test - Calculus 2
This calculus 2 video tutorial provides a basic introduction into the direct comparison test. If the big series converges, then the smaller series must also converge. Likewise, if the small series diverges, the big series must diverge as well. That's the basic idea of the direct compari
From playlist New Calculus Video Playlist
Calculus 2 - Geometric Series, P-Series, Ratio Test, Root Test, Alternating Series, Integral Test
This calculus 2 video provides a basic review into the convergence and divergence of a series. It contains plenty of examples and practice problems. My E-Book: https://amzn.to/3B9c08z Video Playlists: https://www.video-tutor.net Homework Help: https://bit.ly/Find-A-Tutor Subscribe:
From playlist New Calculus Video Playlist
Worldwide Calculus: Theorems on Series II: Non-negative Series
Lecture on 'Theorems on Series II: Non-negative Series' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Direct Comparison Test for Series 3 Examples Calculus 2 BC
I introduce the Direct Comparison Test for Series to help determine if they converge or diverge. The three examples start at 2:39 10:18 15:00 Limit Comparison Test https://www.youtube.com/watch?v=8QyiLX4v4Gw Check out http://www.ProfRobBob.com, there you will find my lessons organized b
From playlist Calculus 2
Intro to series + the integral test
Free ebook http://tinyurl.com/EngMathYT A lecture introducing series and the integral test. Plenty of examples are presented on how to tell if a series converges or diverges. The ideas are seen in university mathematics.
From playlist A second course in university calculus.
Worldwide Calculus: Theorems on Series I: Basic Properties
Lecture on 'Theorems on Series I: Basic Properties' from 'Worldwide Integral Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Financial Time Series Processing
To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technologyconference/ Speaker: Anmol Bajracharya Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices,
From playlist Wolfram Technology Conference 2017
Intro to Infinite Series | Real Analysis
We introduce the definition of infinite series, the definition of a convergent series and the limit of a series, as well as divergent series. We'll discuss partial sums, terms of an infinite series, and look at various examples including geometric series, the harmonic series, and p-series.
From playlist Real Analysis
Absolute Convergence, Conditional Convergence, and Divergence
This calculus video tutorial provides a basic introduction into absolute convergence, conditional convergence, and divergence. If the absolute value of the series convergences, then the original series will converge based on the absolute convergence test. If the absolute value of the ser
From playlist New Calculus Video Playlist