Re: How to enter an integral in a formula and have

*To*: mathgroup at smc.vnet.net*Subject*: [mg108984] Re: How to enter an integral in a formula and have*From*: Leonid Shifrin <lshifr at gmail.com>*Date*: Fri, 9 Apr 2010 03:31:59 -0400 (EDT)

Hi Jim, If you are only interested in numerical values, then the best probably is to explicitly specify that your function <f> expects a numerical input: Clear[f]; f[x_?NumericQ] := NIntegrate[g[y, x], {y, 0, 1}] If you simply want to delay evaluation until the function <f> is called, this is achieved simply by using delayed assignment (SetDelayed): Clear[ff]; ff[x_] := Integrate[g[y, x], {y, 0, 1}] In this case however, every call to <f> will result in re-evaluation of the integral, which may be not what you want (and will be also much slower). Computing your function on a list of values amounts to Map-ping it on this list: In[5]:= Map[f, Range[10]] Out[5]= {1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5} In[6]:= Map[ff,Range[10]] Out[6]= {3/2,5/2,7/2,9/2,11/2,13/2,15/2,17/2,19/2,21/2} Finally, if you want for some reason to work with larger expression where Integrate will be present but will not evaluate, you can enclose the code that produces that expression and works on it, in Block[{Integrate},...]. For example In[7]:= Block[{Integrate},Hold[Evaluate[ff[x]]]] Out[7]= Hold[\!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(1\)]\(\((x + y)\) \[DifferentialD]y\)\)] Once you leave the scope of Block however, all such integrals will evaluate symbolically (that's why I used Hold here to prevent this), so it's up to you then do decide what to do with such an expression. You could, for example, transform it with some set of transformation rules inside Block, according to your needs. Hope this helps. Regards, Leonid On Thu, Apr 8, 2010 at 7:02 AM, Jim Rockford <jim.rockford1 at gmail.com>wrote: > I have a certain integral, part of a larger expression, that can be > expressed in terms of incomplete gamma functions by Mathematica. But > in carrying out the definite integral and forcing it to be written in > terms of gamma functions, this introduces branch points and other > unnecessary complications. I want the integral left alone and > evaluated numerically, but I still want to express the general formula > for this large expression with the unevaluated integral in place. > > For example, I'd like > > f[x_] = (stuff) + int_{0}^{1} (g[s,x]) ds > > where the definite integral is expressed in the usual Mathematica > notation. > > What I do *not* want Mathematica to do at this stage is to do the > integral analytically and write it in terms of special functions. > Instead, I just want to later make a list of values for f[x] and > have the integral done numerically. > > How can I program this? > > Thanks, > Jim > >