Separating integrals

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
1
down vote

favorite












I went across the following equality:



enter image description here



May I ask why does the first line equate to the second line? What is the proof behind that?



Note: $H$ are linear operators. $T$ means that the linear operators are ordered such that operators with lower value of $t$ as their argument are placed on the right.










share|cite|improve this question























  • What is T? $$
    – Sobi
    Sep 2 at 8:36











  • @Sobi I will add this definition to the question
    – Taylor Tiger
    Sep 2 at 8:36






  • 1




    There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
    – GEdgar
    Sep 2 at 12:31














up vote
1
down vote

favorite












I went across the following equality:



enter image description here



May I ask why does the first line equate to the second line? What is the proof behind that?



Note: $H$ are linear operators. $T$ means that the linear operators are ordered such that operators with lower value of $t$ as their argument are placed on the right.










share|cite|improve this question























  • What is T? $$
    – Sobi
    Sep 2 at 8:36











  • @Sobi I will add this definition to the question
    – Taylor Tiger
    Sep 2 at 8:36






  • 1




    There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
    – GEdgar
    Sep 2 at 12:31












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I went across the following equality:



enter image description here



May I ask why does the first line equate to the second line? What is the proof behind that?



Note: $H$ are linear operators. $T$ means that the linear operators are ordered such that operators with lower value of $t$ as their argument are placed on the right.










share|cite|improve this question















I went across the following equality:



enter image description here



May I ask why does the first line equate to the second line? What is the proof behind that?



Note: $H$ are linear operators. $T$ means that the linear operators are ordered such that operators with lower value of $t$ as their argument are placed on the right.







integration






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 2 at 8:37

























asked Sep 2 at 8:34









Taylor Tiger

1168




1168











  • What is T? $$
    – Sobi
    Sep 2 at 8:36











  • @Sobi I will add this definition to the question
    – Taylor Tiger
    Sep 2 at 8:36






  • 1




    There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
    – GEdgar
    Sep 2 at 12:31
















  • What is T? $$
    – Sobi
    Sep 2 at 8:36











  • @Sobi I will add this definition to the question
    – Taylor Tiger
    Sep 2 at 8:36






  • 1




    There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
    – GEdgar
    Sep 2 at 12:31















What is T? $$
– Sobi
Sep 2 at 8:36





What is T? $$
– Sobi
Sep 2 at 8:36













@Sobi I will add this definition to the question
– Taylor Tiger
Sep 2 at 8:36




@Sobi I will add this definition to the question
– Taylor Tiger
Sep 2 at 8:36




1




1




There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
– GEdgar
Sep 2 at 12:31




There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
– GEdgar
Sep 2 at 12:31















active

oldest

votes











Your Answer




StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2902489%2fseparating-integrals%23new-answer', 'question_page');

);

Post as a guest



































active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes















 

draft saved


draft discarded















































 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2902489%2fseparating-integrals%23new-answer', 'question_page');

);

Post as a guest













































































這個網誌中的熱門文章

Is there any way to eliminate the singular point to solve this integral by hand or by approximations?

Why am i infinitely getting the same tweet with the Twitter Search API?

Amount of Number Combinations to Reach a Sum of 10 With Integers 1-9 Using 2 or More Integers [closed]