infinite series with loop in MATLAB

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hasan s 2021-1-21

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评论： hasan s 2021-1-22

采纳的回答： Walter Roberson

how can find F in matlab , where the initial value of z =1

and i is loop from

i=1:10

thanks so much for any help.need code of program if possible

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David Hill 2021-1-22

It is unclear what z array is (from i=1:10) and how i changes in the equation. Should there be another summation on the outside changing i from 1:10?

hasan s 2021-1-22

编辑：hasan s 2021-1-22

thank you for your reply

yes .to chang z

there must summation for i=1:10 ,with initial value to z=1

and another summation k=1:infinity .....for series

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Walter Roberson 2021-1-22

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syms z I k real

F = symsum((-z*I)^k/(k*factorial(k)), k, 1, inf)

F =

However, examine the behavior when k = 0, the lower bound from the equation. The denominator is k*k! which would be 0 * 0! which would be 0*1 which would be 0. So we have a potential problem with singularities, and need to look at the limit. For non-zero z and i, (-z*i)^0 would be 1. Thus we are looking at 1/0 and that is infinite. As that is a term that is included in the actual sum (k = 0 to infinity) we must conclude that F is infinite except for the case where z or i are 0.