ider

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I'm currently addressing a problem related to modified Bessel functions using an older version of Maple (the specific version escapes my memory). In an attempt to resolve issues, I've experimented with the trial version of Maple 2023, but I've encountered an unusual phenomenon. Expressions that were previously simplifiable in Maple now resist simplification. The specific expression provided below, which should equate to 1, fails to be recognized as such by Maple. This poses a concern as it could lead to overly complex expressions in subsequent steps, considering this expression is only an intermediate stage. Is there a recommended approach to overcome this challenge?

f := (BesselI(0, alpha)*alpha-2*BesselI(1, alpha))/(BesselK(0, alpha)*BesselI(1, alpha)*BesselI(0, alpha)*alpha^2+BesselK(1, alpha)*BesselI(0, alpha)^2*alpha^2-2*BesselI(1, alpha))

(BesselI(0, alpha)*alpha-2*BesselI(1, alpha))/(BesselK(0, alpha)*BesselI(1, alpha)*BesselI(0, alpha)*alpha^2+BesselK(1, alpha)*BesselI(0, alpha)^2*alpha^2-2*BesselI(1, alpha))

simplify(f)

(BesselI(0, alpha)*alpha-2*BesselI(1, alpha))/(BesselK(0, alpha)*BesselI(1, alpha)*BesselI(0, alpha)*alpha^2+BesselK(1, alpha)*BesselI(0, alpha)^2*alpha^2-2*BesselI(1, alpha))

eval(f, alpha = .25)

1.000000000

NULL

Download question.mw

I am using Maple to compute the principal part around the point 0, which involves obtaining the series expansion terms with strictly negative powers. This is necessary for my work on evaluating infinite integrals that involve complex functions. While I can calculate these expressions manually, I am exploring whether Maple already offers a convenient tool for this purpose. For instance, Maple's built-in Laurent series expansion can be used to obtain the principal part of functions like BesselK(4, x) as 48/x^4 - 4/x^2. Any assistance on this matter is greatly appreciated. Thank you for your help.

For instance, Hypergeometric0F1Regularized^(1,0)[1,1.] = -0.113894... as given in Mathematica. I was wondering how this type of regularized hypergeometric function is defined in Maple. 

While I was elaborating on a math problem, I came across the following expression which actually should be equal to one. Maple unfortunately was unable to fully provide a simplified expression. Is there a way to do that? 

Thank you

Consider the following integral, shown below in this image.

>> Link to the Maple sheet: example.mw <<

Why does Maple provide erroneous results? Is there a bug in the software? I use Maple 2021.

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