ewce09.azraftaohid.me/L2T2/MATH 203/SA/Termology.md

Created: 2025/04/07 09:13

Term	Description
Absolutely convergent	An infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series $[PARSE ERROR: Undefined("Command(\"displaystyle\")")] [PARSE ERROR: Undefined("Command(\"textstyle\")")] \sum_{n = 0}^{\infty} a_{n} [PARSE ERROR: Undefined("Command(\"textstyle\")")] \sum_{n = 0}^{\infty} a_{n}$ is said to converge absolutely if $[PARSE ERROR: Undefined("Command(\"displaystyle\")")] [PARSE ERROR: Undefined("Command(\"textstyle\")")] \sum_{n = 0}^{\infty} \| a_{n} \| = L [PARSE ERROR: Undefined("Command(\"textstyle\")")] \sum_{n = 0}^{\infty} \| a_{n} \| = L$ for some real number $[PARSE ERROR: Undefined("Command(\"displaystyle\")")] [PARSE ERROR: Undefined("Command(\"textstyle\")")] L .$
Absolutely intregreable	A function whose absolute value is integrable, meaning that the integral of the absolute value over the whole domain is finite.

Term

Description

Absolutely convergent

An infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series

[PARSE ERROR: Undefined("Command(\"displaystyle\")")] [PARSE ERROR: Undefined("Command(\"textstyle\")")] \sum_{n = 0}^{\infty} a_{n} [PARSE ERROR: Undefined("Command(\"textstyle\")")] \sum_{n = 0}^{\infty} a_{n}

is said to converge absolutely if

[PARSE ERROR: Undefined("Command(\"displaystyle\")")] [PARSE ERROR: Undefined("Command(\"textstyle\")")] \sum_{n = 0}^{\infty} | a_{n} | = L [PARSE ERROR: Undefined("Command(\"textstyle\")")] \sum_{n = 0}^{\infty} | a_{n} | = L

for some real number

[PARSE ERROR: Undefined("Command(\"displaystyle\")")] [PARSE ERROR: Undefined("Command(\"textstyle\")")] L .

Absolutely intregreable

A function whose absolute value is integrable, meaning that the integral of the absolute value over the whole domain is finite.