# symbolic operations

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## 1—10 of 38 matching pages

##### 2: 34.9 Graphical Method
The graphical method establishes a one-to-one correspondence between an analytic expression and a diagram by assigning a graphical symbol to each function and operation of the analytic expression. …
##### 3: 1.17 Integral and Series Representations of the Dirac Delta
This is a symbolic function with the properties: …Such a sequence is called a delta sequence and we write, symbolically, … In the language of physics and applied mathematics, these equations indicate the normalizations chosen for these non-$L^{2}$ improper eigenfunctions of the differential operators (with derivatives respect to spatial co-ordinates) which generate them; the normalizations (1.17.12_1) and (1.17.12_2) are explicitly derived in Friedman (1990, Ch. 4), the others follow similarly. …
##### 4: Guide to Searching the DLMF
Search queries are made up of terms, textual phrases, and math expressions, combined with Boolean operators:
• term:

a textual word, a number, or a math symbol.

• Boolean operator:

and and or

• proximity operator:

adj, prec/n, and near/n, where n is any positive natural number.

##### 5: 18.38 Mathematical Applications
A further operator, the so-called Casimir operator
###### Dunkl Type Operators and Nonsymmetric Orthogonal Polynomials
The Dunkl operator, introduced by Dunkl (1989), is an operator associated with reflection groups or root systems which has terms involving first order partial derivatives and reflection terms. … In the one-variable case the Dunkl operator eigenvalue equation … …
##### 6: 17.6 ${{}_{2}\phi_{1}}$ Function
17.6.25 $\mathcal{D}_{q}^{n}{{}_{2}\phi_{1}}\left({a,b\atop c};q,zd\right)=\frac{\left(% a,b;q\right)_{n}d^{n}}{\left(c;q\right)_{n}(1-q)^{n}}{{}_{2}\phi_{1}}\left({aq% ^{n},bq^{n}\atop cq^{n}};q,dz\right),$
17.6.26 $\mathcal{D}_{q}^{n}\left(\frac{\left(z;q\right)_{\infty}}{\left(abz/c;q\right)% _{\infty}}{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)\right)=\frac{\left(c/a% ,c/b;q\right)_{n}}{\left(c;q\right)_{n}(1-q)^{n}}\left(\frac{ab}{c}\right)^{n}% \frac{\left(zq^{n};q\right)_{\infty}}{\left(abz/c;q\right)_{\infty}}{{}_{2}% \phi_{1}}\left({a,b\atop cq^{n}};q,zq^{n}\right).$
##### 7: 18.42 Software
Also included is a website (CAOP) operated by a university department. … A more complete list of available software for computing these functions, and for generating formulas symbolically, is found in the Software Index. …
##### 8: 17.2 Calculus
17.2.42 $f^{[n]}(z)=\mathcal{D}_{q}^{n}f(z)=\begin{cases}z^{-n}(1-q)^{-n}\sum_{j=0}^{n}% q^{-nj+\genfrac{(}{)}{0.0pt}{}{j+1}{2}}(-1)^{j}\genfrac{[}{]}{0.0pt}{}{n}{j}_{% q}f(zq^{j}),&z\neq 0,\\ \dfrac{f^{(n)}(0)\left(q;q\right)_{n}}{n!(1-q)^{n}},&z=0.\end{cases}$
##### 9: 26.22 Software
Also included are websites operated by university departments and consortia, research institutions, and peer-reviewed journals. …
• Inverse Symbolic Calculator (website).

• ##### 10: About MathML
As a general rule, using the latest available version of your chosen browser, plugins and an updated operating system is helpful. … Since the display of mathematics involves many special symbols not often seen in plain text, a MathML renderer generally needs special fonts. … For other browsers, you may see a ? or a box like indicating missing symbols, and thus insufficient fonts. …