Difference between revisions of "Hahn-Exton q-Bessel"
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(Created page with "The Hahn-Exton $q$-Bessel function, also called the Jackson $q$-Bessel function $J_{\nu}^{(3)}$, is defined by $$J_{\nu}^{(3)}(x;q)=\dfrac{x^{\nu}(q^{\nu+1};q)_{\infty}}{(q;q)...") |
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The Hahn-Exton $q$-Bessel function, also called the Jackson $q$-Bessel function $J_{\nu}^{(3)}$, is defined by | The Hahn-Exton $q$-Bessel function, also called the Jackson $q$-Bessel function $J_{\nu}^{(3)}$, is defined by | ||
$$J_{\nu}^{(3)}(x;q)=\dfrac{x^{\nu}(q^{\nu+1};q)_{\infty}}{(q;q)_{\infty}} \displaystyle\sum_{k \geq 0}\dfrac{(-1)^kq^{\frac{k(k+1)}{2}}x^{2k}}{(q^{\nu+1};q)_k(q;q)_k}.$$ | $$J_{\nu}^{(3)}(x;q)=\dfrac{x^{\nu}(q^{\nu+1};q)_{\infty}}{(q;q)_{\infty}} \displaystyle\sum_{k \geq 0}\dfrac{(-1)^kq^{\frac{k(k+1)}{2}}x^{2k}}{(q^{\nu+1};q)_k(q;q)_k}.$$ | ||
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Latest revision as of 18:54, 24 May 2016
The Hahn-Exton $q$-Bessel function, also called the Jackson $q$-Bessel function $J_{\nu}^{(3)}$, is defined by $$J_{\nu}^{(3)}(x;q)=\dfrac{x^{\nu}(q^{\nu+1};q)_{\infty}}{(q;q)_{\infty}} \displaystyle\sum_{k \geq 0}\dfrac{(-1)^kq^{\frac{k(k+1)}{2}}x^{2k}}{(q^{\nu+1};q)_k(q;q)_k}.$$
