查看“︁QBeta函数”︁的源代码

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'''qBeta函数'''是[[B函数]]的q模拟

:<math>B_q(a,b)=\frac{\Gamma_q(a)\cdot \Gamma_q(b)}{\Gamma_q(a+b)}</math>

其中<math>\Gamma_q(a)</math>是[[QΓ函数]]。

當<math>b > 0</math>且<math>a \neq 0, -1, -2, \ldots</math>時，該函數亦可以{{le|q積分|q-Integral|''q''積分}}和[[q階乘冪|''q''階乘冪]]定義：<ref name = "salem">{{cite journal|title = Generalized ''q''-integrals via neutrices: Application to the ''q''-beta function|author = Ahmed Salem|journal = Filomat|volume = 27|issue = 8|year = 2013|pages = 1473–1483|doi = 10.2298/FIL1308473S|publisher = Faculty of Sciences and Mathematics, {{le|University of Niš
}}, Serbia}}</ref>{{rp|1481}}
:<math>B_q(a, b) = \int_0^1 x^{b-1} \frac{(qx;q)_\infty}{(q^a x;q)_\infty}\mathrm{d}_q x.</math>

其與[[基本超几何函数]]<math>{}_2\phi_1</math>的關係為：<ref name = "salem"/>{{rp|1482}}
:<math>B_q(a, b) = {}_2\phi_1(q^{1-a}, q^b;q^{b+1};q, q^a).</math>

==参考文献==
<references/>
*{{cite book|author = Frank Oliver|title = NIST Handbook of Mathematical Functions|page = 145|publisher = Cambridge University Press|year = 2010}}

== 外部鏈結 ==
{{MathWorld |id= q-BetaFunction|title= q-Beta Function}}
[[Category:伽玛及相关函数]]
[[Category:Q-模拟]]
{{q超几何函数}}