Abel test is a mathematical concept used to determine the convergence of an infinite series. It is named after the Norwegian mathematician, Niels Henrik Abel, who developed the test in the early 19th century. The Abel test is a useful tool in calculus and analysis, and it is widely used in various fields of mathematics.
Definitions
The Abel test is a convergence test for infinite series. It states that if a series of functions is uniformly convergent, then the series of integrals of those functions is also convergent. In other words, if the limit of the series of functions converges, then the limit of the series of integrals of those functions also converges.
Origin
The Abel test is named after Niels Henrik Abel, who was a Norwegian mathematician born in 1802. Abel made significant contributions to the fields of algebra, analysis, and number theory. He developed the Abel test in the early 19th century, and it has since become an essential tool in calculus and analysis.
Meaning in different dictionaries
According to the Oxford English Dictionary, the Abel test is “a test for the convergence of an infinite series, stating that if a series of functions is uniformly convergent, then the series of integrals of those functions is also convergent.”
The Merriam-Webster Dictionary defines the Abel test as “a test for the convergence of an infinite series that depends on the convergence of the series of integrals of the terms of the given series.”
Associations
The Abel test is associated with various mathematical concepts, including convergence, infinite series, and integrals. It is commonly used in calculus and analysis, and it is essential in determining the convergence of complex mathematical equations.
Synonyms
There are no synonyms for the Abel test, as it is a specific mathematical concept with a unique name.
Antonyms
There are no antonyms for the Abel test, as it is a mathematical concept that cannot be opposed or negated.
The same root words
The Abel test does not share any root words with other mathematical concepts or terms.
Example Sentences
- The Abel test is a useful tool in determining the convergence of infinite series.
- Without the Abel test, it would be challenging to solve complex mathematical equations.
- The Abel test is named after Niels Henrik Abel, a renowned Norwegian mathematician.
- The Abel test is an essential concept in calculus and analysis.
- The Abel test is used to determine the convergence of a series of integrals of functions.