implement first kind bessel function

2019 10 18
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更新时间：2019 10 21
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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?

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Walter Roberson
Walter Roberson 2019-10-18

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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.

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