# Infinite Sequences and Series: Power Series

0

• 9
• 0
• 0.158
• Reply

• Published on Jun 12, 2020
###### About :

In this video I go over further into infinite sequences and series and this time look at the Power Series which is a series in which a power function is being summed up. The power series has many useful applications such as the vibrations of a drum as in the Bessel function and has to do with the particular behavior of the power series to oscillate in large amplitudes initially and dissipate with distance and/or time. I go over many examples, exercises, and proofs in yet another epic long math video, so follow along to learn more!

The topics and their timestamps in the video are listed below:

1. @ 1:54 - Power Series
• @ 9:41 - Note on Trigonometric Series and the Fourier Series
• @ 10:40 - Example 1
• @ 14:33 – Note on Factorials
• @ 15:23 - Example 2
2. @ 24:31 - Note on Bessel Functions
• @ 25:49 - Example 3: Bessel Function of Order 0
3. @ 49:41 - Theorem 1
• @ 55:54 - Summary of Previous Examples
• @ 58:35 - Example 4
• @ 1:07:22 - Example 5
4. Exercises
• @ 1:17:18 - Exercise 1: Bessel Function of Order 1
• @ 1:34:44 - Exercise 2: Proof of Theorem 1
• @ 1:35:53 - Theorem 2
• @ 1:49:24 - Theorem 3
• @ 1:53:48 - Completeness Axiom

Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIh_ZL0WExNvIL4J0s2Q?e=GkZR2u

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-power-series

Related Videos:

Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz

Infinite Sequences: Limits, Squeeze Theorem, Fibonacci Sequence & Golden Ratio + MORE: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more

Infinite Series: Definition, Examples, Geometric Series, Harmonics Series, Telescoping Sum + MORE: https://peakd.com/mathematics/@mes/infinite-series-definition-examples-geometric-series-harmonics-series-telescoping-sum-more

Infinite Sequences and Series: The Integral Test and Estimate of Sums: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-the-integral-test-and-estimate-of-sums

Infinite Sequences and Series: The Comparison Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-the-comparison-tests

Infinite Sequences and Series: Alternating Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-alternating-tests

Infinite Sequences and Series: Absolute Convergence and the Ratio/Root Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-absolute-convergence-and-the-ratio-root-tests

Infinite Sequences and Series: Strategy for Testing Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-strategy-for-testing-series .

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Hive: https://peakd.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: contact@mes.fm

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

###### Reply:

To comment on this video please connect a HIVE account to your profile: Connect HIVE Account

09:19
5 views a year ago \$
10:52
5 views a year ago \$
04:09:08
1 views a year ago \$
30:08
0 views a year ago \$
16:36
2 views a year ago \$

#### More Videos

07:35
1 views a month ago \$
01:22
7 views 7 months ago \$
01:04:45
6 views a year ago \$
13:44
0 views 4 months ago \$
01:07
7 views 2 years ago \$
07:49
10 views 2 years ago \$
01:53
2 views 7 months ago \$
08:42
8 views a year ago \$
04:30
2 views a year ago \$
00:40
3 views a year ago \$
06:18
0 views 3 months ago \$
01:10:34
0 views 6 months ago \$
05:42
6 views 2 years ago \$
09:09
4 views a year ago \$
09:24
0 views 2 years ago \$
04:27
9 views 3 months ago \$
21:53
2 views a year ago \$
10:38
4 views 2 years ago \$
06:46
19 views 3 weeks ago \$
04:38
1 views a year ago \$
03:13
5 views 2 years ago \$
06:51
0 views a year ago \$
21:12
3 views a year ago \$
12:50
4 views 2 years ago \$
02:41
0 views 2 years ago \$