4

I don't know if this has already been discussed.

Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}, Assumptions -> m ϵ Integers]

ConditionalExpression[1, Re[m] > -1]

Integrate[BesselJ[2 m, x], {x, 0, ∞}, Assumptions -> m ϵ Integers]

ConditionalExpression[1, Re[m] > -(1/2)]

Assuming[m ∈ Integers, Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}]]

ConditionalExpression[1, m > -1]

Assuming[m ∈ Integers, Integrate[BesselJ[2 m, x], {x, 0, ∞}]]

ConditionalExpression[1, m > -(1/2)]

Why doesn't Mathematica consider the evenness or oddness of the 1st argument (i.e., 2 m or 2 m + 1)?

m_goldberg
  • 107,779
  • 16
  • 103
  • 257
Dimitris
  • 4,794
  • 22
  • 50
  • @Karsten 7: Thanks for the edit. – Dimitris Oct 16 '15 at 08:53
  • 2
    Related (possibly duplicates): (19833), (42114) -- See this answer to (19833) especially. – Michael E2 Oct 16 '15 at 10:12
  • 1
    Thanks for the links. However here the situation is different. Assuming[{k ∈ Integers}, Integrate[ Exp[ I k t], {t, -π, π}]] returns an incorrect result whereas Integrate[ Exp[ I k t], {t, -π, π},Assumptions->k ∈ Integers] returns the correct one. Here it seams that Integrate simply ignores (or cannot take into account) the Assumptions and proceed to its evaluation of the integrand without any Assumptions for both of the cases. – Dimitris Oct 16 '15 at 12:10
  • 1
    I think Daniel's answer explains it: Try Simplify[Integrate[Exp[I k t], {t, -\[Pi], \[Pi]}, Assumptions -> k \[Element] Integers], k \[Element] Integers]. – Michael E2 Oct 16 '15 at 13:03
  • I agree with @MichaelE2. – Daniel Lichtblau Oct 16 '15 at 14:48
  • Michael and Daniel thanks for the comments. I read many times Daniel's reply but still I cannot understand what it is the connection with the current situation. Can you elaborate more in this issue? For me is like Integrate cannot utilize the included Assumptions so it treats Integrate[BesselJ[2 m, x], {x, 0, ∞}, Assumptions -> m ϵ Integers] as simple Integrate[BesselJ[2 m, x], {x, 0, ∞}]. Am I correct? – Dimitris Oct 16 '15 at 14:57
  • sorry, what is the expected result? Is this page wrong too? http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/21/02/01/ – george2079 Oct 16 '15 at 17:21
  • Daniel's answer implies that the Assuming result should be like the one in which you Simplify the Assumptions result like this: With[{res = Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}, Assumptions -> m ∈ Integers]}, Assuming[m ∈ Integers, Simplify[res]]], which it is. (If $Assumptions is used elsewhere in computing the integral, one might get other differences, too, I suppose.) See also this, which coincidentally came up a little after your question. – Michael E2 Oct 17 '15 at 02:31

0 Answers0