Using Negative Range for Bessel Function Results in 2 Values

Question

I am using the inbuilt function of matlab to calculate the bessel function of second order, following is the code

format long
z = (-5:1:5)';

 y = bessely(1,z)
plot (y)

The output is as follows

y =

-0.147863143391227 + 0.655158275182930i

-0.397925710557100 + 0.132086656047098i

-0.324674424791800 - 0.678117917051873i

0.107032431540937 - 1.153449615513747i

0.781212821300289 - 0.880101171489867i

           -Inf                       

-0.781212821300289
-0.107032431540937
0.324674424791800
0.397925710557100
0.147863143391227

What i don't understand is why am i getting two values when the value of z is negative ?

Answer 1

This

-0.147863143391227 + 0.655158275182930i

is not two values, it's a single complex number. See the i at the right of the second part ? That's Matlab's way of telling you that that second number is the imaginary part of the number, the one which is multiplied by i, the square root of -1.

Matlab is telling you, and I concur with Matlab on this, that that function returns complex values for negative inputs.

Answer 2

Two values?! It's a complex number! That is, a number of the form x+yi, where i is the square root of -1.