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Question: An Integral to be done from 1911

Question:An Integral to be done from 1911

Dr. Zaninetti Lorenzo 40 Maple
integration
May 18 2020
2

The following spreadsheet contains an integral to be done

in the framework of the Maxwell–Jüttner distribution and therefore date back to 1911

integrale_juttner_primes.mw
 

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restart;
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with(IntegrationTools):

the following integrand represents the scaling of the Maxwell–Jüttner distribution (1911) in 3D

where x is the Lorentz factor which is equal or greater than 1

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integrandx:= x*sqrt(x^2 - 1)*exp(-x);

x*(x^2-1)^(1/2)*exp(-x)

 (1)
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C:=1/int(integrandx,x=1..infinity);

1/(BesselK(0, 1)+2*BesselK(1, 1))

 (2)
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pdf:=C*integrandx;

x*(x^2-1)^(1/2)*exp(-x)/(BesselK(0, 1)+2*BesselK(1, 1))

 (3)

the above pdf represents the probability density function of the Maxwell–Jüttner distribution

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DF:=int(C*integrandx,x=1..xx) assuming xx>1;

int(x*(x^2-1)^(1/2)*exp(-x)/(BesselK(0, 1)+2*BesselK(1, 1)), x = 1 .. xx)

 (4)

the above DF represents the inert form of the distribution function but the integral at the moment

does not exists

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