How to create this function in Matlab?

I want to write a mathematical function in matlab so that I can call it in my program whenever needed.

? a(n).b(n)/sqrt((a(n)^2) + (b(n)^2))

n=0 to limit. The limit is approx 1000.

a and b are 1 dimensional matrix. size of a and b is : (1xlimit)

[Matt Fig]

What is this: a(n).b(n)

is that supposed to be: a(n)*b(n)

[Walter Roberson]

Is the '?' the summation operator?

[vish]

Sorry, the '?' is a summation operator. Its still showing me the operator but I believe the symbol is not recognizable in other computers.

summation of n=0 to limit...

summation of a(n)*b(n)/(sqrt((a(n)^2) + (b(n)^2)))

limit is the size of matrix a and b.

[vish]

I will try to explain in a better way. if x= 4 then i want to do

a(1)*b(1)/(sqrt((a(1)^2) + (b(1)^2))) + a(2)*b(2)/(sqrt((a(2)^2) + (b(2)^2))) + a(3)*b(3)/(sqrt((a(3)^2) + (b(3)^2))) + a(4)*b(4)/(sqrt((a(4)^2) + (b(4)^2))).

In my actual program the value of x is more than 1000, so its not possible for me to do it manually. I am sorry I cudnt explain properly earlier.

a and b are 1x4 matrix

[Matt Fig]

Did you try the codes below?

[vish]

Thanks, I just tried it. Its working. Matlabs really powerful. I am grateful for showing me the snippet.

Answer 1

[Walter Roberson]

Assuming the '?' is the summation operator, then:

sum(a.*b./sqrt(a.^2 + b.^2))

[Matt Fig]

Beat me too it! I was too slow deciphering the question, I guess.

Answer 2

[Matt Fig]

If I understand you correctly,

function S = mysum(a,b)
S = sum(a.*b./sqrt(a.^2 + b.^2));

EDIT

.

. Sean de points out known stability issues with square roots of the sum of squares.

function S = mysum(a,b)
S = sum(a.*b./hypot(a,b));

[Sean de Wolski]

I would use:

./hypot(a,b)

[Matt Fig]

That too...