Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: Gauss multiplication formula

Bottom of Page

1 to 3 of 3

- 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
- 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 $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>⋅</mo><msup><mi>N</mi> <mrow><mstyle displaystyle="false"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle><mo>−</mo><mi>N</mi><mi>z</mi></mrow></msup><mo>⋅</mo><mi>Γ</mi><mo stretchy="false">(</mo><mi>N</mi><mi>z</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\cdot N^{ \tfrac{1}{2} - N z } \cdot \Gamma( N z )</annotation></semantics></math>$ doesn’t return to the baseline. Is this a bug in the layout engine?
$<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><munderover><mo lspace="0.16667em" rspace="0.16667em">∏</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></munderover><mi>Γ</mi><mrow><mo>(</mo><mi>z</mi><mo>+</mo><mstyle displaystyle="false"><mfrac><mi>j</mi><mi>N</mi></mfrac></mstyle><mo>)</mo></mrow><mspace width="0.27778em"/><mo>=</mo><mspace width="0.27778em"/><mo stretchy="false">(</mo><mn>2</mn><mi>π</mi><msup><mo stretchy="false">)</mo> <mrow><mstyle displaystyle="false"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle><mo stretchy="false">(</mo><mi>N</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msup><mo>⋅</mo><msup><mi>N</mi> <mrow><mstyle displaystyle="false"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle><mo>−</mo><mi>N</mi><mi>z</mi></mrow></msup><mo>⋅</mo><mi>Γ</mi><mo stretchy="false">(</mo><mi>N</mi><mi>z</mi><mo stretchy="false">)</mo><mspace width="0.16667em"/><mo>.</mo></mrow><annotation encoding="application/x-tex"> \underoverset {j = 0} {N-1} {\prod} \Gamma \left( z + \tfrac{j}{N} \right) \;=\; (2 \pi)^{ \tfrac{1}{2}(N-1) } \cdot N^{ \tfrac{1}{2} - N z } \cdot \Gamma( N z ) \,. </annotation></semantics></math>$
- 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 $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo stretchy="false">/</mo><mn>2</mn><mo>−</mo><mi>N</mi><mi>z</mi></mrow><annotation encoding="application/x-tex">1/2 - N z</annotation></semantics></math>$ really is meant to be in the exponent? I should maybe put this in parenthesis. Will do.)

1 to 3 of 3

nForum

Discussion Feed

Not signed in

Site Tag Cloud

nLab > Latest Changes: Gauss multiplication formula