Guide to Searching the DLMF
Overview
In DLMF, you can search not only for text but also for mathematical expressions. Every page contains a search box in the navigation bar. From there you can also access an advanced search page where you can control certain settings, narrowing the search to certain chapters, or restricting the results to equations, graphs, tables, or bibliographic items.
Query  Matching records contain 

"Fourier transform" and series 
both the phrase “Fourier transform” and the word “series”. 
Fourier or series 
at least one of the words “Fourier” or “series”. 
Fourier (transform or series) 
at least one of “Fourier transform” or “Fourier series”. 
1/(2pi) and "Fourier transform" 
both $1/(2\pi )$ and the phrase “Fourier transform”. 
sin^2 +cos^2 
the expression ${\mathrm{sin}}^{2}+{\mathrm{cos}}^{2}$. 
J_n(z)= 
the math fragment ${J}_{n}(z)=$ 
J_n@(z)= 
the math fragment ${J}_{n}(z)=$, emphasizing more that ${J}_{n}$ is a function. 
J_n@(x or z)= 
at least one of the math fragments ${J}_{n}(x)=$ or ${J}_{n}(z)$, emphasizing that ${J}_{n}$ is a function. 
int sin 
the integral of the sin function 
int_$^$ sin 
any definite integral of sin 
sin x and (J_nu(z) or I_nu(z)) 
both $\mathrm{sin}x$ and at least one of the two functions ${J}_{\nu}(z)$ or ${I}_{\nu}(z)$. 
DeMoivre and cos (n theta) 
both the word “DeMoivre” and the expression $\mathrm{cos}(n\theta )$. 
BesselJ_nu and BesselY_nu 
both the Bessel functions ${J}_{\nu}$ and ${Y}_{\nu}$. 
Euler 
the word ”Euler” or any of the various Euler terms such as Euler Gamma function $\mathrm{\Gamma}$, Euler Beta function $\mathrm{B}$, etc. 
trigonometric 
the word ”trigonometric” or any of the various trigonometric functions such as $\mathrm{sin}$, $\mathrm{cos}$, $\mathrm{tan}$, and $\mathrm{cot}$. 
trig$ 
any word that matches the pattern “trig$ ”, that is, that starts with “trig”,
such as “trigonometric” and “trigonometry”, including the various trigonometric functions such as $\mathrm{sin}$ and $\mathrm{cos}$. 
trigonometric^2 + trig$^2 
any sum of the squares of two trigonometric functions such as ${\mathrm{sin}}^{2}z+{\mathrm{cos}}^{2}z$. 


int adj sin 
$\int $ immediately followed by $\mathrm{sin}$ without any intervening terms. 
int prec/10 sin(x) 
$\int $ preceding $\mathrm{sin}x$ by no more than 10 terms. 
Gamma near/5 = 
the terms $\mathrm{\Gamma}$ and = such that $\mathrm{\Gamma}$ is up to 5 terms before or after = . 
(int adj sin(x)) near/5 = 
the subexpression $\int \mathrm{sin}$ and = , in whatever order and separated by no more than 5 terms. 
More Details
Terms, Phrases and Expressions
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.
 phrase:

any doublequoted sequence of textual words and numbers.
 math expression:

any LaTeXlike sequence of terms, excluding phrases.
 Boolean operator:

and and or
 proximity operator:

adj, prec/n, and near/n, where n is any positive natural number.
All terms are taken to be caseinsensitive, except those taken to represent math expressions (see Case Sensitivity).
Wildcards
Wildcards allow matching patterns and marking parts of an expression that don’t matter (as for example, which variable name the author uses for a function):
$ 
stands for any number of alphanumeric characters 

(the more conventional * is reserved for the multiplication operator) 

? 
stands for any zero or one alphanumeric character. 
(If ? occurs as a separate token, it effectively acts like $ ) 
Query  What it stands for 

sin? 
sin, sine, sinh, sinc, … 
si$ 
si, sin, sine, sinh, sinc, sinInt, similar, … 
co$te 
Coordinate, conjugate, correlate,… 
B$l? 
Bessel, BesselJ, BesselI, BesselK, Bernoulli,… 
int_$^$ sin 
any definite integral of sin. 
Query relaxation
If a query does not return any hits, the DLMF search system relaxes
the query to match and retrieve what may be intended by the original query.
For example, the expression ${\mathrm{Ai}}^{2}+{\mathrm{Bi}}^{2}$ does not occur verbatim in DLMF,
but ${\mathrm{Ai}}^{2}\left(z\right)+{\mathrm{Bi}}^{2}\left(z\right)$ and ${\mathrm{Ai}}^{2}\left(x\right)+{\mathrm{Bi}}^{2}\left(x\right)$ do.
Therefore, if your query is Ai^2+Bi^2
, the system modifies the query
so it will find the equations containing the latter expressions.
Fine Points in Math Search
To recognize the math symbols and structures, and to accommodate equivalence between various notations and various forms of expression, the search system maps the math part of your queries into a different form. If you do not want a term or a sequence of terms in your query to undergo math processing, you should quote them as a phrase. Be careful, however, because if you put quotes around math expressions involving math symbols, you may not get the matches you’d expect.
Math Symbols
You can use in math queries all the symbols and commands defined in LaTeX (you can omit the $\backslash $), and some additional convenient ones, as well as the special functions’ names:
Symbols  Comments 

=, , +, *, /, >, < 

<=, >= 
For $\le $ and $\ge $. 
+, + 
For $\pm $ and $\mp $ 
_, ^ 
For subscripting and superscripting (power) 
' (single quote) 
As a prime, which can stand for the derivative 
>, <, <>, =>, <==, <=> 
For arrows $\to $, $\leftarrow $, $\leftrightarrow $, $\Rightarrow $, $\Leftarrow $ and $\iff $ 
~ 
For similarto $\sim $ 
~~ 
For approximation $\approx $. 
= 
For equivalence $\equiv $ 
All elementary functions  Such as sin, cos, tan, Ln, log, exp 
All names of special functions  Such as BesselI, BesselJ, LegendreP, KummerU, etc. 
The syntax of the special functions can be LaTeXlike or as employed in widely
used computer algebra systems. For example, for the Bessel function ${K}_{n}\left(z\right)$,
you can write K_n(z)
, BesselK_n(z)
, BesselK(n,z)
, or BesselK[n,z]
.
Note that the first form may match other functions $K$ than the Bessel $K$ function,
so if you are sure you want Bessel $K$, you might as well enter one of the other 3 forms.
Case Sensitivity
DLMF search is generally caseinsensitive except when it is important to be casesensitive, as when two different special functions have the same standard names but one name has a lowercase initial and the other is has an uppercase initial, such as si and Si, gamma and Gamma. In the following situations, DLMF search is casesensitive:

•
Singleletter terms

•
All the Greek Letters (gamma vs. Gamma, sigma vs. Sigma, etc.)

•
All the inverse trigonometric functions (arcsin vs. Arcsin, etc.).

•
The following standard special functions: si, Si, ci, Ci, shi, Shi, ce, Ce, se, Se, ln, Ln, Lommels, LommelS, Jacobiphi, and the list is still growing.
Fonts and Accents
Sometimes there are distinctions between various special function names based on font style, such as the use of bold or calligraphic letters. DLMF search recognizes just the essential font differences, that is, the font style differences deemed important for the DLMF contents:
Query  Matches 

cal L 
$\mathcal{L}$ 
bold H 
$\mathbf{H}$ 
theta hat 
$\widehat{\theta}$ 
U bar 
$\overline{U}$ 
B tilde 
$\stackrel{~}{B}$ 
If you don’t specify the font style or font accessories in the query, the style and accessories won’t matter in the search, but if you specify them, they will matter.
Metadata for More Effective Search
To find more effectively the information you need, especially equations, you may at times wish to specify what you want with descriptive words that characterize the contents but do not occur literally. For example, you may want equations that contain trigonometric functions, but you don’t care which trigonometric function. The natural thing is to enter the query trigonometric, and expect to have all the right matches. DLMF search provides this feature, which it accomplishes through the use of metadata.