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Question: Why doesn't evalf return a number?

Question:Why doesn't evalf return a number?

Angelo Melino 45 Maple 2024
syntax 2dmath evalf
February 10 2025
0

In trying to evaluate the accuracy of an asymptotic approximation, I asked evalf to return the numerical value of the difference of two expressions.  It evaluated each expression but would not take their difference (see line 6).  Any idea what's going on?

restart

g := exp(-r*cosh(x))*x^(2*n); G := Int(g, x = 0 .. infinity)

Int(exp(-r*cosh(x))*x^(2*n), x = 0 .. infinity)

 (1)

f0 := arccosh(1+y); df0 := diff(f0, y)

1/(y^(1/2)*(2+y)^(1/2))

 (2)

f := f0^(2*n)*df0

arccosh(1+y)^(2*n)/(y^(1/2)*(2+y)^(1/2))

 (3)

n := 2; series(f, y)

2*2^(1/2)*y^(3/2)-(7/6)*2^(1/2)*y^(5/2)+(47/80)*2^(1/2)*y^(7/2)-(17281/60480)*2^(1/2)*y^(9/2)+O(y^(11/2))

 (4)

r := 6; evalf(G)

0.8560816424e-4

 (5)

Ghat := exp(-r)*(2*sqrt(2)*GAMMA(5/2)*`-`*(7*sqrt(2)*(1/6))/r^(5/2)*(GAMMA(7/2)/r^(7/2))); Ghat1 := evalf(Ghat)

0.1056905544e-3-0.2568867641e-4*``

 (6)

evalf(Ghat1)

0.1056905544e-3-0.2568867641e-4*``

 (7)

 

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