limit involving multi-arg function (polygamma) fails

[smichr]

h[2] >>> polygamma(2,3)
    polygamma(2, 3)
    h[3] >>> _.n()
    -0.154113806319189
    h[4] >>> limit(polygamma(2+1/x,3+exp(-x)),x,oo)
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
      File "sympy\series\limits.py", line 186, in limit
        r = gruntz(e, z, z0, dir)
      File "sympy\series\gruntz.py", line 473, in gruntz
        return limitinf(e, z)
      File "sympy\series\gruntz.py", line 340, in limitinf
        return limitinf(c0, x) #e0=0: lim f = lim c0
      File "sympy\series\gruntz.py", line 328, in limitinf
        c0, e0 = mrv_leadterm(e, x)
      File "sympy\series\gruntz.py", line 390, in mrv_leadterm
        mrv_leadterm_up = mrv_leadterm(e_up, x, Omega_up)
      File "sympy\series\gruntz.py", line 402, in mrv_leadterm
        series = calculate_series(f, w)
      File "sympy\series\gruntz.py", line 364, in calculate_series
        series = f.nseries(x, n=n).removeO()
      File "sympy\core\expr.py", line 1394, in nseries
        return self._eval_nseries(x, n=n)
      File "sympy\core\function.py", line 315, in _eval_nseries
        e = e.diff(x)
      File "sympy\core\expr.py", line 1499, in diff
        return Derivative(self, *new_symbols, **assumptions)
      File "sympy\core\function.py", line 601, in __new__
        obj = expr._eval_derivative(s)
      File "sympy\core\function.py", line 266, in _eval_derivative
        df = self.fdiff(i)
      File "sympy\functions\special\gamma_functions.py", line 156, in fdiff
        raise ArgumentIndexError(self, argindex)
    NameError: global name 'ArgumentIndexError' is not defined

Original issue for #5415: http://code.google.com/p/sympy/issues/detail?id=2316
Original author: https://code.google.com/u/117933771799683895267/
Original owner: https://code.google.com/u/117933771799683895267/

[smichr]

**Summary:** limit involving multi-arg function (polygamma) fails  

Original comment: http://code.google.com/p/sympy/issues/detail?id=2316#c1
Original author: https://code.google.com/u/117933771799683895267/

[rlamy]

The first argument of polygamma has to be an integer, so the limit is meaningless. The error message could be nicer though. The problem with ArgumentIndexError is issue 4853 .

Referenced issues: #4853
Original comment: http://code.google.com/p/sympy/issues/detail?id=2316#c2
Original author: https://code.google.com/u/101272611947379421629/

[asmeurer]

**Status:** Valid  

Original comment: http://code.google.com/p/sympy/issues/detail?id=2316#c3
Original author: https://code.google.com/u/asmeurer@gmail.com/

[skirpichev]

Now the error is "NotImplementedError: MRV set computation for functions in several variables not implemented."  Looks better, I think.

**Labels:** Series  

Original comment: http://code.google.com/p/sympy/issues/detail?id=2316#c4
Original author: https://code.google.com/u/113518207426301808764/

[hacman]

I'm wondering what is involved in fixing this. I got a similar error ("NotImplementedError: MRV set ...") when trying to evaluate

>>> num = binomial(2*n,n)/(n+1)
>>> denom = 4**n/sqrt(pi*n**3)
>>> limit(num/denom, n, oo)
<NotImplementedError>

If I tell sympy to use the factorial definition of the binomial coefficient, I get the right answer:
>> num = factorial(2*n)/factorial(n)**2/(n+1)
>>> denom = 4**n/sqrt(pi*n**3)
>>> limit(num/denom, n, oo)
1

What's slightly special about this case is that the error relating to several variables does not really apply. Since I am evaluating a quantity that, while defined in terms of a binomial coefficient, is really a univariate expression. So my questions are twofold:

1. what is involved in getting full multivariate support?
2. if that is too difficult, is it worth attempting to simplify expressions that are actually univariate? I believe that .free_symbols would work here)

Original comment: http://code.google.com/p/sympy/issues/detail?id=2316#c5
Original author: https://code.google.com/u/111461499536629158271/

[pelegm]

The following looks like the same issue:

>>> n = Symbol('n', integer=True, positive=True)
>>> limit(binomial(n, n/2), n, oo)

raises

Traceback (most recent call last):
  File "<ipython-input-4-f56a9c6c64d3>", line 1, in <module>
    limit(binomial(n, n/2), n, oo)
  File "sympy/series/limits.py", line 42, in limit
    return Limit(e, z, z0, dir).doit(deep=False)
  File "sympy/series/limits.py", line 157, in doit
    r = gruntz(e, z, z0, dir)
  File "sympy/series/gruntz.py", line 641, in gruntz
    r = limitinf(e, z)
  File "sympy/core/cache.py", line 91, in wrapper
    retval = cfunc(*args, **kwargs)
  File "sympy/core/compatibility.py", line 872, in wrapper
    result = user_function(*args, **kwds)
  File "sympy/series/gruntz.py", line 424, in limitinf
    c0, e0 = mrv_leadterm(e, x)
  File "sympy/core/cache.py", line 91, in wrapper
    retval = cfunc(*args, **kwargs)
  File "sympy/core/compatibility.py", line 872, in wrapper
    result = user_function(*args, **kwds)
  File "sympy/series/gruntz.py", line 480, in mrv_leadterm
    Omega, exps = mrv(e, x)
  File "sympy/series/gruntz.py", line 295, in mrv
    raise NotImplementedError("MRV set computation for functions in"
NotImplementedError: MRV set computation for functions in several variables not implemented.