请输入您要查询的字词:

 

单词 LaplaceTransformOfPowerFunction
释义

Laplace transform of power function


In the defining integralDlmfPlanetmath (http://planetmath.org/ImproperIntegral)

{tr}=0e-sttr𝑑t

of the Laplace transformDlmfMathworldPlanetmath of the power functionDlmfDlmfPlanetmathttr,  we make the substitution (http://planetmath.org/SubstitutionForIntegration)  u:=st:

{tr}=0e-u(us)rdus=1sn+10e-uur+1-1𝑑u

Here we have assumed that  r>-1  and s>0.  According to the definition of the gamma functionDlmfDlmfMathworldPlanetmath, the last integral is equal toΓ(r+1).  Thus we obtain

{tr}=Γ(r+1)sr+1.(1)

The special case  r=-12  gives the result

{1t}=πs.(2)
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 16:18:25