Sum of products of polylogarithm function











up vote
0
down vote

favorite












I want to find a nice expression of sum of products of polylogarithm function



begin{align}
sumlimits_{k_1+k_2+cdots+k_m=k\ k_1,k_2,ldots,k_mge 1}Li_{k_1}(x)Li_{k_2}(x)cdots Li_{k_m}(x)=?
end{align}
It have a short expression?






summation products







share|cite|improve this question







New contributor




xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • Try to convert it into a single nice multiplication that contains the sum of the k's
    – Moti
    15 hours ago















up vote
0
down vote

favorite












I want to find a nice expression of sum of products of polylogarithm function



begin{align}
sumlimits_{k_1+k_2+cdots+k_m=k\ k_1,k_2,ldots,k_mge 1}Li_{k_1}(x)Li_{k_2}(x)cdots Li_{k_m}(x)=?
end{align}
It have a short expression?






summation products







share|cite|improve this question







New contributor




xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • Try to convert it into a single nice multiplication that contains the sum of the k's
    – Moti
    15 hours ago













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I want to find a nice expression of sum of products of polylogarithm function



begin{align}
sumlimits_{k_1+k_2+cdots+k_m=k\ k_1,k_2,ldots,k_mge 1}Li_{k_1}(x)Li_{k_2}(x)cdots Li_{k_m}(x)=?
end{align}
It have a short expression?






summation products







share|cite|improve this question







New contributor




xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I want to find a nice expression of sum of products of polylogarithm function



begin{align}
sumlimits_{k_1+k_2+cdots+k_m=k\ k_1,k_2,ldots,k_mge 1}Li_{k_1}(x)Li_{k_2}(x)cdots Li_{k_m}(x)=?
end{align}
It have a short expression?






summation products




summation products






share|cite|improve this question







New contributor




xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question







New contributor




xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question






New contributor




xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 16 hours ago









xuce1234

112




112




New contributor




xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • Try to convert it into a single nice multiplication that contains the sum of the k's
    – Moti
    15 hours ago


















  • Try to convert it into a single nice multiplication that contains the sum of the k's
    – Moti
    15 hours ago
















Try to convert it into a single nice multiplication that contains the sum of the k's
– Moti
15 hours ago




Try to convert it into a single nice multiplication that contains the sum of the k's
– Moti
15 hours ago















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: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});






xuce1234 is a new contributor. Be nice, and check out our Code of Conduct.










 

draft saved


draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2995405%2fsum-of-products-of-polylogarithm-function%23new-answer', 'question_page');
}
);

Post as a guest























active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes








xuce1234 is a new contributor. Be nice, and check out our Code of Conduct.










 

draft saved


draft discarded


















xuce1234 is a new contributor. Be nice, and check out our Code of Conduct.













xuce1234 is a new contributor. Be nice, and check out our Code of Conduct.












xuce1234 is a new contributor. Be nice, and check out our Code of Conduct.















 


draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2995405%2fsum-of-products-of-polylogarithm-function%23new-answer', 'question_page');
}
);

Post as a guest






































































-

Popular posts from this blog

How to change which sound is reproduced for terminal bell?

Image
3 Recently upgrade to 18.10 from 18.04, and using the terminal is becoming annoying: the new alert sound is a drip ( /usr/share/sounds/gnome/default/alerts/drip.ogg ), and the previous one is still located at ( /usr/share/sounds/ubuntu/stereo/bell.ogg ). My issue is that at the gnome-terminal, when autocompleting or pressing left BOTH sounds are reproduced, at the same time. I want to just have ubuntu/stereo/bell.ogg active, not both . At the moment I have been only able to reduce the volume of the alerts (but still both are played), or turn the alerts down (but I dislike both "solutions"). gnome-terminal 18.10 teminal-bell share | improve this question
Read more

Can I use Tabulator js library in my java Spring + Thymeleaf project?

Image
0 I want to add Tabulator js to my java project. I added tabulator.min.js, tabulator.min.css to resources folder. After that added to my html page these dependencies as recommending in readme.md. <link rel="stylesheet" th:href="@{/css/tabulator.min.css}"> <script type="text/javascript" th:src="@{/js/tabulator.min.js}"></script> Now my tables view all elements, that I have in the html page, but not correct. In the documentation of Tabulator is example how to create header and table, var table = new Tabulator("#example-table", { columns:[ {title:"Name", field:"name", sorter:"string", width:200, editor:true}, {title:"Age", field:"age", sorter:"
Read more

Title Spacing in Bjornstrup Chapter, Removing Chapter Number From Contents

Image
up vote 5 down vote favorite 2 I would like to make it so that the vertical space below the title of each chapter is the same when using the Bjornstrup package (i.e. so that the descenders do not affect the spacing - as shown by the red arrow in the picture below). I think I'm fairly happy with the spacing around "A chapter", so I'd really like titles without descenders (e.g. "Contents") to have the same vertical spacing as "A chapter" below the title. I would also like to remove the large "0" in the contents title. Any help appreciated, as always. documentclass[11pt,a4paper]{book} % Packages[![enter image description here][1]][1] usepackage[left=3.5cm, right=3.5cm, top=4.3cm, bottom=4.25cm]{geometry} usepackage[utf8]{inputenc} usepackage{libertine} usepackage[libertine]{newtx
Read more