Jackson q-Bessel function: Difference between revisions
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en>Headbomb m Various citation cleanup (identifiers mostly), replaced: | url=http://dx.doi.org/10.1016/0022-247X → | doi=10.1016/0022-247X, | id={{JFM|36.0513.02}} → | jfm=36.0513.02, | id={{MR|649849}} → | mr=649849 using AWB |
en>Anrnusna m →References: journal name, replaced: Trans. Roy. Soc. Edinburgh → Transactions of the Royal Society of Edinburgh (2), Edinb. Roy. Soc. Trans. → Transactions of the Royal Society of Edinburgh, Proc. London Math. Soc. using AWB |
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[[Image:Powers chart.png|thumb|Exponentiation of numbers 0-10. Line labels = base. X axis = power. Y axis = result.]] | |||
In [[exponentiation]], the '''base''' is the number <var>b</var> in an expression of the form <var>b<sup>n</var></sup>. The number <var>n</var> is called the [[exponent]] and the expression is known formally as exponentiation of <var>b</var> by <var>n</var> or the exponential of <var>n</var> with base <var>b</var>. It is more commonly expressed as "the <var>n</var>th power of <var>b</var>", "<var>b</var> to the <var>n</var>th power" or "<var>b</var> to the power <var>n</var>". For example, the fourth power of 10 is 10000 since 10<sup>4</sup> = 10000. The term ''power'' strictly refers to the entire expression, but is sometimes used to refer to the exponent. | |||
When the <var>n</var>th power of <var>b</var> equals a number <var>a</var>, or <var>a = b<sup>n</sup></var> , then <var>b</var> is called an "[[nth root|<var>n</var>th root]]" of <var>a</var>. For example, 10 is a fourth root of 10000. | |||
The [[inverse function]] to exponentiation with base <var>b</var> (when it is [[well-defined]]) is called the [[logarithm]] to base <var>b</var>, denoted log<sub><var>b</var></sub>. Thus: | |||
:<math>\log_b a = n. \, </math> | |||
For example, <math>\log_{10} 10000 = 4</math>. | |||
==See also== | |||
*[[Radix]] | |||
[[Category:Exponentials]] | |||
Revision as of 03:10, 18 October 2013
In exponentiation, the base is the number b in an expression of the form bn. The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power" or "b to the power n". For example, the fourth power of 10 is 10000 since 104 = 10000. The term power strictly refers to the entire expression, but is sometimes used to refer to the exponent.
When the nth power of b equals a number a, or a = bn , then b is called an "nth root" of a. For example, 10 is a fourth root of 10000.
The inverse function to exponentiation with base b (when it is well-defined) is called the logarithm to base b, denoted logb. Thus:
For example, .
