从所周知,欧拉不等式2r≤R2(3)^(1/3)r≤3^(1/3)R。(1765)我们可加细到2(3)^(1/3)r≤(abc)1/3≤1/3(a+b+c)≤3^(1/3)R;(1)2(3)^(1/3)r≤(abc)^(1/3)≤{P integral from n=1 to ∞(+8)[(a+x)(b+x)(c+x)]^-(P+1)3dx}-1/P≤1/3(a+b+c)≤3^(...从所周知,欧拉不等式2r≤R2(3)^(1/3)r≤3^(1/3)R。(1765)我们可加细到2(3)^(1/3)r≤(abc)1/3≤1/3(a+b+c)≤3^(1/3)R;(1)2(3)^(1/3)r≤(abc)^(1/3)≤{P integral from n=1 to ∞(+8)[(a+x)(b+x)(c+x)]^-(P+1)3dx}-1/P≤1/3(a+b+c)≤3^(1/3)R;(2)2(3)^(1/3)≤(abc)^(1/3){P integral from n=1 to ∞(+8)[(a+x)(b+x)(c+x)]^-(P+1)/3dx}^-(1/P)≤{Pintegral from n=1 to ∞(+8)λ^(-1)[(ι+λ)(a+x))^(1/3)(ι+λ(b+x))^(1/3)(ι+λ(c+x))^(1/3)-ι]^(-P-1)dx}^(-1/P)≤1/3(a+b+c)≤3^(1/3)R。(3)展开更多
文摘从所周知,欧拉不等式2r≤R2(3)^(1/3)r≤3^(1/3)R。(1765)我们可加细到2(3)^(1/3)r≤(abc)1/3≤1/3(a+b+c)≤3^(1/3)R;(1)2(3)^(1/3)r≤(abc)^(1/3)≤{P integral from n=1 to ∞(+8)[(a+x)(b+x)(c+x)]^-(P+1)3dx}-1/P≤1/3(a+b+c)≤3^(1/3)R;(2)2(3)^(1/3)≤(abc)^(1/3){P integral from n=1 to ∞(+8)[(a+x)(b+x)(c+x)]^-(P+1)/3dx}^-(1/P)≤{Pintegral from n=1 to ∞(+8)λ^(-1)[(ι+λ)(a+x))^(1/3)(ι+λ(b+x))^(1/3)(ι+λ(c+x))^(1/3)-ι]^(-P-1)dx}^(-1/P)≤1/3(a+b+c)≤3^(1/3)R。(3)
