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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 1st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexPage created, but author did not leave any comments. <a href="https://ncatlab.org/nlab/revision/Gauss+multiplication+formula/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Gauss+multiplication+formula">current</a>

   Page created, but author did not leave any comments.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorRodMcGuire
   • CommentTimeJun 1st 2021
   • PermaLink
   Author: RodMcGuire
   Format: MarkdownItexSomething is wrong in your formula where $\cdot N^{ \tfrac{1}{2} - N z } \cdot \Gamma( N z )$ doesn't return to the baseline. Is this a bug in the layout engine? $$ \underoverset {j = 0} {N-1} {\prod} \Gamma \left( z + \tfrac{j}{N} \right) \;=\; (2 \pi)^{ \tfrac{1}{2}(N-1) } \cdot N^{ \tfrac{1}{2} - N z } \cdot \Gamma( N z ) \,. $$

   Something is wrong in your formula where $\cdot N^{ \tfrac{1}{2} - N z } \cdot \Gamma( N z )$ doesn’t return to the baseline. Is this a bug in the layout engine?

   $$\underoverset {j = 0} {N-1} {\prod} \Gamma \left( z + \tfrac{j}{N} \right) \;=\; (2 \pi)^{ \tfrac{1}{2}(N-1) } \cdot N^{ \tfrac{1}{2} - N z } \cdot \Gamma( N z ) \,.$$
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 1st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexOn my system (Firefox 88.0.1) it looks correct. (Are you taking into account that all of $1/2 - N z$ really is meant to be in the exponent? I should maybe put this in parenthesis. Will do.)

   On my system (Firefox 88.0.1) it looks correct. (Are you taking into account that all of $1/2 - N z$ really is meant to be in the exponent? I should maybe put this in parenthesis. Will do.)