Sum of products of polylogarithm function











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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







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















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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







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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
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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






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asked 16 hours ago









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xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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xuce1234 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • 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















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