Difference between revisions of "Euler-Jackson q-difference operator"
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(Created page with "The Euler-Jackson $q$-difference operator applied to a function $f$ is given by the formula $$(D_q f)(x)=\dfrac{f(x)-f(qx)}{(1-q)x}.$$") |
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| − | The Euler-Jackson $q$-difference operator applied to a function $f$ is given by the formula | + | Let $q \in \mathbb{C} \setminus \{1\}$. The Euler-Jackson $q$-difference operator applied to a function $f$ is given by the formula |
$$(D_q f)(x)=\dfrac{f(x)-f(qx)}{(1-q)x}.$$ | $$(D_q f)(x)=\dfrac{f(x)-f(qx)}{(1-q)x}.$$ | ||
Latest revision as of 20:04, 3 June 2016
Let $q \in \mathbb{C} \setminus \{1\}$. The Euler-Jackson $q$-difference operator applied to a function $f$ is given by the formula $$(D_q f)(x)=\dfrac{f(x)-f(qx)}{(1-q)x}.$$
