implement first kind bessel function

I want to implement bessel function of first kind in MATLAB.

• Jo = First kind zero order.
• J1 There is nothing mentioned what is J1 in the artcile
• But wikipidea says: The series indicates that −J1(x) is the derivative of J0(x),
• What is J1 and how should i implement in MATLAB?
• Should r be a constant value or variable?

Let us say I want to implement Jo(r) and J1(r)

Jo = besselj(0,r);
J1 = -besselj(1,r);

is the code J1 correct?

Answer 1

[Walter Roberson]

Not exactly. Although -J1 is the derivative of J0, that does not mean that J1 = -besselj(1,x), it means that J1 = besselj(1,x) and that the derivative of J0 happens to change sign.

Analogy: diff(cos(x), x) = -sin(x) but that doesn't mean that you define cos(x) with an inherent - sign.

[sai reddy]

Thank you Walter. OK. I follow the same.