CODEWITHSUNDEEP
pythonsympyderivative
riki_tiki
riki_tiki

Reputation: 13

higher order derivative in Sympy problem with dummy indecis

How to get kth derivative of f(x) where k is also a dummy index in summation. sym.diff(f,x,n) is interpreted as derivative of f with respect to both x and k not as kth derivative of f(x) which is what I want. The problem I have is in this expression

sym.Sum((1/sym.factorial(k)*sym.diff(fun,x,k)*(x-a)**k),(k,0,10))

Any suggestions? I want to some over kth derivatives as in taylor series, however, I don't know how to make sympy interpret k as number - order of the derivative (coming from the summation) and not a variable when it comes to the differentiation. The problem: how sum evaluates to zero

Mistake isn't inside the sum

Upvotes: 1

Views: 327

Answers (1)

Oscar Benjamin
Oscar Benjamin

Reputation: 14500

I'm not sure I understand what you want but I guess you need to pass a tuple (x, k) like diff(f, (x, k)) rather than diff(f, x, k). Like this:

In [1]: import sympy as sym

In [2]: x, k, a = sym.symbols('x, k, a')

In [3]: fun = Function('f')(x)

In [4]: sym.Sum((1/sym.factorial(k)*sym.diff(fun,(x,k))*(x-a)**k),(k,0,10))
Out[4]: 
  10                      
______                    
╲                         
 ╲                        
  ╲                k      
   ╲           k  d       
    ╲  (-a + x) ⋅───(f(x))
    ╱              k      
   ╱             dx       
  ╱    ───────────────────
 ╱              k!        
╱                         
‾‾‾‾‾‾                    
k = 0 

In [5]: _.doit()
Out[5]: 
            10                      9                     8                     7                     6                     5                
        10 d                    9  d                  8  d                  7  d                  6  d                  5  d                 
(-a + x)  ⋅────(f(x))   (-a + x) ⋅───(f(x))   (-a + x) ⋅───(f(x))   (-a + x) ⋅───(f(x))   (-a + x) ⋅───(f(x))   (-a + x) ⋅───(f(x))   (-a + x
             10                     9                     8                     7                     6                     5                
           dx                     dx                    dx                    dx                    dx                    dx                 
───────────────────── + ─────────────────── + ─────────────────── + ─────────────────── + ─────────────────── + ─────────────────── + ───────
       3628800                 362880                40320                  5040                  720                   120                  

     4                     3                     2                                 
 4  d                  3  d                  2  d                                  
) ⋅───(f(x))   (-a + x) ⋅───(f(x))   (-a + x) ⋅───(f(x))                           
     4                     3                     2                                 
   dx                    dx                    dx                   d              
──────────── + ─────────────────── + ─────────────────── + (-a + x)⋅──(f(x)) + f(x)
  24                    6                     2                     dx

Upvotes: 2

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