摘要
在计算弹性薄板时.常需要计算一些无穷级数的极限和.本文给出形如sum from m=1 to ∞(sin (mπξ)/a sin (mπx)/a)/(m^4+2ηm^2(a^2/π~2)+(p^2(a^4/π~4)))一类级数在η~2=p^2,η~2>p^2,η~2<p^2三种情况下的极限和表达式。
To calculate the elastic thin plates,we must abtain the sums of some infinite serieses.In this paper,we obtain the sum of series sum from m=1 to ∞ (sin(mπ/α)sin/(mπx/α))/(m^4+2ηm^2(α~2/π~2)+p^2(α~4/π~4))in the cases η~2=p^2,η~2>p^2,η~2<p^2.
关键词
级数
极限和
弹性地基
梁
无究级数
series
sum of series
Beam on the elastic foundation.