Jackson q-Bessel function: Difference between revisions

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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
en>Rjwilmsi
m →References: Added 1 doi to a journal cite using AWB (10434)
 
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{{Calculation results}}
[[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.
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When the <var>n</var>th power of <var>b</var> equals a number <var>a</var>, or  &nbsp;<var>a&nbsp;=&nbsp;b<sup>n</sup></var>&nbsp;, 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]]

Latest revision as of 14:30, 9 September 2014

\ոI'm a 46 years old, married and work at the university (Anthropology аnd Sociology).
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