The simplest (default) usage of this page is to graph up to five functions (and up to four parametric curves, and up to four polar curves) on a specified window, in essentially the same way that most graphing calculators do: by plotting points and playing "connect the dots" to approximate the curve of the function.

The more advanced features let you change the number of points plotted, and choose an "adaptive" approach that attempts to determine where more points are needed to create a smooth curve. (So far, this adaptive approach only applies to functions, not polar and parametric curves.) You can also have the computer attempt to identify step discontinuities (so that it does not "connect the dots" at such points).

In addition to standard functions (exp, sqrt, cos, sin, ln, etc.), a few more advanced functions are available. Click a link to see Wikipedia's information about these functions:

• gamma(x) and lngamma(x) — the gamma function and its logarithm
• incgamma(a,x) and incgammainv(a,p) — the regularized incomplete gamma function, called P(s,x) at Wikipedia, and its inverse function
• digamma(x) — the logarithmic derivative of the gamma function
• beta(a,b) and lnbeta(a,b) — the beta function and its logarithm
• incbeta(x,a,b) and incbetainv(x,a,b) — the regularized incomplete beta function, and its inverse function
• zeta(x) — the Riemann zeta function
• fresnelc(x) and fresnels(x) — the Fresnel cosine and sine functions
• erf(x) and erfc(x) — the error function and its complement
• hypgeom(a,b,c,x) — the Gaussian (ordinary) hypergeometric function ₂F₁(a,b;c;x)
• cantor(x) — the Cantor function (also called the Devil's staircase)
• blanc(x,a) — the blancmange (Takagi) curve, with an optional parameter a between 0 and 1. (The parameter is my own invention, not mentioned on the Wikipedia page.)
• weierstrass(x,a,b) — Weierstrass's nowhere-differentiable function. If omitted, a = 0.5 and b = 3. It's virtually impossible to get a good graph, but interesting to explore nonetheless.

In fact, this page was first developed because I needed to implement some of those functions in JavaScript, and I wanted a simple way to see if they were returning the correct values. Please note that while these functions are good enough for general exploration, they are only approximations (with typical accuracy in the range of 6–10 significant figures). Also, definitions of some of these functions vary slightly, so my implementation might not exactly match that on the Wikipedia page. (In particular, the name "Weierstrass function" is given to lots of nowhere-differentiable functions; I picked one…and I am not 100% sure I implemented it correctly.)

(December 19, 2013) First release: This page has been tested on Chrome (fairly extensively), Firefox (less), and Explorer (minimally).

(January 12, 2014) Lots of new functions added, along with the ability to compose functions (including a "safety feature" to prevent inadvertently causing an infinite recursion). Trying to track down a bug with adaptive plotting for the incbetainv function.

(October 13, 2014) Parametric and polar plotting added, and (October 16) incorporated into the "bookmark" link.

(May 22, 2015) Links can now be shared on Facebook without being mangled.

TODO (someday): Add shade above/below (maybe); more functions (exponential integral, sine/cosine integral, ...), add adaptive plotting to polar and parametric curves.

The contents of this page are © 2014 Darryl Nester. It is available to anyone who wishes to use it (like most things on the Internet). Please send me an email if you have found it to be useful, or if you have suggestions.