Plot[ Sum [Sum[ ]]] not working in Wolfram|Alpha

Questions
,
1

I have this simple query:

plot sum((21-n)^(it)*(21-n)^(sum(i^m * pi^m/factorial(m)) for m=1 to n)) for n=2 to 19, t=0 to 40

for which the response is “Wolfram alpha can not understand the query ‘sum sum’”

However, it can perfectly understand

plot sum((21-n)^(sum(i^m * pi^m/factorial(m)) for m=1 to n)) for n=2 to 19, t=0 to 40

As I need the first query response, how to tweak it so that WA can understand the query?

Thanks
Bhargavi

2

Ask WolframAlpha to evaluate

(21-n)^(it)*(21-n)^Sum[i^m*pi^m/m!,{m,1,n}]

Click to see the Mathematica plain text that you can scrape

(21-n)^(-1+I t-Gamma[1+n,I Pi]/Gamma[1+n])

Copy and paste that to ask WolframAlpha to evaluate

Plot[Sum[(21-n)^(-1+I t-Gamma[1+n,I Pi]/Gamma[1+n]),{n,2,19}],{t,0,40}]

and you get

Your desired plot

I hope I have correctly understood what you are trying to calculate.