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Question: what's wrong with the integration

Question:what's wrong with the integration

zippon 55 Maple 15
integration
February 16 2013
0

I have a function

 int(exp(-(ln(p)-mu)^2/(2*sigma^2))/(sqrt(2*Pi)*sigma*p)*((k*x/p)^(k-1)*exp(-k*x/p)*k/(p*GAMMA(k))), p = 0 .. infinity)

where mu=-19.89674583,sigma=2.35671007 and k=2.475778082 are parameters

I calculate the integration of s with respect of x on intervals of 10^((-120.5+i)*(1/10)) .. 10^((-119.5+i)*(1/10))

(i  is from 0 to 96)

I find that when i=53,the result is 5.563104178*10^(-15),while i=54,the result is 5.046055397*10^(-3).

The funtion is smooth but the variation is about 12 orders.what's wrong with the integration?

s := proc (x, k, mu, sigma) options operator, arrow; int(exp(-(1/2)*(ln(p)-mu)^2/sigma^2)*(k*x/p)^(k-1)*exp(-k*x/p)*k/(sqrt(2*Pi)*sigma*p*p*GAMMA(k)), p = 0 .. infinity) end proc: 

v := `<,>`(seq(10^((-120.5+i)*(1/10)), i = 0 .. 96)):``NULL

T1 := `<,>`(seq(int(s(t, 2.475778082, -19.89674583, sqrt(5.554082353)), t = 10^((-120.5+i)*(1/10)) .. 10^((-119.5+i)*(1/10))), i = 0 .. 96))

RTABLE(295221112, anything, Vector[column], rectangular, Fortran_order, [], 1, 1 .. 97)

 (1)

int(s(t, 2.475778082, -19.89674583, sqrt(5.554082353)), t = 10^((1/10)*(-120.5+53)) .. 10^((1/10)*(-119.5+53)))

0.5563104178e-14

 (2)

int(s(t, 2.475778082, -19.89674583, sqrt(5.554082353)), t = 10^((1/10)*(-120.5+54)) .. 10^((1/10)*(-119.5+54)))

0.5046055397e-2

 (3)

plot(s(x, 2.475778082, -19.89674583, sqrt(5.554082353)), x = 10^((1/10)*(-120.5+52)) .. 10^((1/10)*(-119.5+55)))

  

``


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