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I want to know the order of divergence.

S_n=∫_{-1→1}dz∫_{a→n}dx∫_{a→n}dyh(x,y,z), where a>0, n is a real number,
h(x,y,z)=zx^3y^3/{f(x)f(y)}(1/E(x)+1/E(y)){1/L(x,y,z)}^4, f(x)=√(x^2+c^2), c>0,
E(x)=x^2/(2m)+f(x), L(x,y,z)=(x^2+y^2+2xyz)/(2m)+f(x)+f(y).
When n →∞, does the inegral diverge or converge? If it diverges, what order does it diverge?
Please explain in detail.

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suugakujyuku

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Answers (1)

Question I want to know the order of divergence. Question I want to know the order of divergence.
S_n=∫_{-1→1}dz∫_{a→n}dx∫_{a→n}dyh(x,y,z), where a>0, n is a real number,
h(x,y,z)=zx^3y^3/{f(x)f(y)}(1/E(x)+1/E(y)){1/L(x,y,z)}^4, f(x)=√(x^2+c^2), c>0,
E(x)=x^2/(2m)+f(x), L(x,y,z)=(x^2+y^2+2xyz)/(2m)+f(x)+f(y).
When n →∞, does the inegral diverge or converge? If it diverges, what order does it diverge?
Please explain in detail.
No img2

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