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Minimum of the upper limit of a summation

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AVM 2020-6-13

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编辑： AVM 2020-6-13

采纳的回答： Ameer Hamza

I would like to write the summation

in the matlab code where

are positive integer. Can anyone help me how to write that in matlab?

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Ameer Hamza 2020-6-13

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在 MATLAB Online 中打开

Something like this

p = 10;
q = 12;
up_lim = min(p, q);
f = @(x) sum((x-1).^(0:up_lim));

Result

>> f(0)
ans =
     1
>> f(0.5)
ans =
    0.6670
>> f(1)
ans =
     1
>> f(2)
ans =
    11
>> f(5)
ans =
     1398101

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Thanks a lot.

Ameer Hamza 2020-6-13

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I am glad to be of help!

AVM 2020-6-13

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编辑：AVM 2020-6-13

How does f(1)=1? because at x=1, f(x)=x-1 =0. Pl let me know.

Ameer Hamza 2020-6-13

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MATLAB defines 0^0 as 1. Do you want to use some other value?

AVM 2020-6-13

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Thanks. No need. Actually I have to use this code for other things. I think it's enough.

Stephen23 2020-6-13

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编辑：Stephen23 2020-6-13

In many (but not all) branches of mathematics, the agreed value of 0^0 is 1.

This definition is also common in many (but not all) programming languages.

https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero

AVM 2020-6-13

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@Stephen: Thanks for your information.

AVM 2020-6-13

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@Ameer: If the p and q be the sym variables, then can I use the same code? If not, pl tell me what will be the corresponding code for symbolic summation. I need that.

Ameer Hamza 2020-6-13

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在 MATLAB Online 中打开

Comparison operators are not defined for symbolic variables, so you cannot use min() for p and q. However, you can do something like this

syms up_lim x s;
f(x) = symsum((x-1)^s, s, 0, up_lim);

AVM 2020-6-13

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But here, as ''up_lim'' is itself a sym variable, so the defination up_lim=min(p,q) is not utilized. It looks like that I can replace ''up_lim'' by some symbolic variable as n. But Is there any way to call ''min(p,q)?. Pl inform me.