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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeOct 21st 2011
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   Author: zskoda
   Format: MarkdownItexNew entry [[special function]], extensions to [[hypergeometric function]], [[Selberg integral]]. New entries [[gamma function]], recently also [[Euler beta function]]. Stub for [[elementary function]].

   New entry special function, extensions to hypergeometric function, Selberg integral. New entries gamma function, recently also Euler beta function.

   Stub for elementary function.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeOct 22nd 2011
   • (edited Oct 22nd 2011)
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   Author: Todd_Trimble
   Format: MarkdownItexAt [[elementary function]], I've never seen 'transcendental' defined that way; I thought that meant a function that isn't algebraic, e.g., $e^x$ or $\sin(x)$. I can't remember seeing anything other than 'non-elementary' (or something similar) for a function not in the class of elementary functions.

   At elementary function, I’ve never seen ’transcendental’ defined that way; I thought that meant a function that isn’t algebraic, e.g., $e^x$ or $\sin(x)$. I can’t remember seeing anything other than ’non-elementary’ (or something similar) for a function not in the class of elementary functions.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeOct 22nd 2011
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   Author: Todd_Trimble
   Format: MarkdownItexI changed the title from 'gamma function' to [[Gamma function]], and added some material.

   I changed the title from ’gamma function’ to Gamma function, and added some material.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeOct 22nd 2011
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   Author: zskoda
   Format: MarkdownItexYou are right about transcendental ! This way as you say is used by algebraic geometers, and this is now dominant. In special functions, it was sometimes in earlier times used the way I said, but the algebraic geometry usage is now far dominant. It should be corrected. For Gamma vs. gamma I would not quite agree. Some of the modern monographs on special functions which I read these days use gamma and beta when spelling the name in full, without capitals. In fact I do not recall ever seen it other way around. This has nothing to do with the capitalization of the notation, which is pretty consistent for gamma and inconsistent for Euler beta in the literature. Of course, following the notation in spelling has some information and is not a bad idea. I hope we will have much more in those entries in $n$Lab soon...

   You are right about transcendental ! This way as you say is used by algebraic geometers, and this is now dominant. In special functions, it was sometimes in earlier times used the way I said, but the algebraic geometry usage is now far dominant. It should be corrected.

   For Gamma vs. gamma I would not quite agree. Some of the modern monographs on special functions which I read these days use gamma and beta when spelling the name in full, without capitals. In fact I do not recall ever seen it other way around. This has nothing to do with the capitalization of the notation, which is pretty consistent for gamma and inconsistent for Euler beta in the literature. Of course, following the notation in spelling has some information and is not a bad idea.

   I hope we will have much more in those entries in $n$Lab soon…

5. • CommentRowNumber5.
   • CommentAuthorTodd_Trimble
   • CommentTimeOct 22nd 2011
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   Author: Todd_Trimble
   Format: MarkdownItexYou're probably right about Gamma/gamma -- I was looking quickly at Andrews-Askey-Roy and see they have Gamma in chapter/section titles, but gamma within the text (I haven't gone through this super-carefully). I thought Gamma was more logical, but I'll leave it for you to decide. Sorry for the change!

   You’re probably right about Gamma/gamma – I was looking quickly at Andrews-Askey-Roy and see they have Gamma in chapter/section titles, but gamma within the text (I haven’t gone through this super-carefully). I thought Gamma was more logical, but I’ll leave it for you to decide. Sorry for the change!

6. • CommentRowNumber6.
   • CommentAuthorTobyBartels
   • CommentTimeOct 22nd 2011
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   Author: TobyBartels
   Format: MarkdownItexArguably, the proper name is ‘$\Gamma$ function’ and our naming conventions then require us to put the page at [[Gamma function]] as the nearest approximation without special characters.

   Arguably, the proper name is ‘$\Gamma$ function’ and our naming conventions then require us to put the page at Gamma function as the nearest approximation without special characters.

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeOct 24th 2011
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   Author: zskoda
   Format: MarkdownItexI do not know of "arguably" argument in recording the language conventjons. The way the language is it is. the name gamma function is used when the spelling is in full, i.e. in primary form. Calling it $\Gamma$-function is just an abbreviation.

   I do not know of “arguably” argument in recording the language conventjons. The way the language is it is. the name gamma function is used when the spelling is in full, i.e. in primary form. Calling it $\Gamma$-function is just an abbreviation.

8. • CommentRowNumber8.
   • CommentAuthorColin Tan
   • CommentTimeJan 23rd 2014
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   Author: Colin Tan
   Format: TextCan each constant function be "obtained from the identity function, the power functions, trigonometric functions, the exponential functions and logarithmic functions by the algebraic operations and composition"? I guess we have to require constant functions as part of the initial data to define the class of elementary functions.

   Can each constant function be "obtained from the identity function, the power functions, trigonometric functions, the exponential functions and logarithmic functions by the algebraic operations and composition"? I guess we have to require constant functions as part of the initial data to define the class of elementary functions.
9. • CommentRowNumber9.
   • CommentAuthorDavidRoberts
   • CommentTimeJan 23rd 2014
   • (edited Jan 23rd 2014)
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   Author: DavidRoberts
   Format: MarkdownItexsin² x + cos² x = 1, and surely linear combinations count...

   sin² x + cos² x = 1, and surely linear combinations count…

10. • CommentRowNumber10.
    • CommentAuthorColin Tan
    • CommentTimeJan 23rd 2014
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    Author: Colin Tan
    Format: TextAt present, the Lab entry describes algebraic operations as the ring operations. Spitulating closure under complex linear combinations is equivalent to inserting the constant functions as initial data.

    At present, the Lab entry describes algebraic operations as the ring operations. Spitulating closure under complex linear combinations is equivalent to inserting the constant functions as initial data.
11. • CommentRowNumber11.
    • CommentAuthorzskoda
    • CommentTimeJan 23rd 2014
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    Author: zskoda
    Format: MarkdownItexCome on, multiplication with a scalar is an algebraic operation.

    Come on, multiplication with a scalar is an algebraic operation.

12. • CommentRowNumber12.
    • CommentAuthorTodd_Trimble
    • CommentTimeJan 23rd 2014
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    Author: Todd_Trimble
    Format: MarkdownItexI've gone ahead and included the constant functions in the article, to remove any doubt. (The article hadn't included multiplication by a scalar, which of course should be there.)

    I’ve gone ahead and included the constant functions in the article, to remove any doubt. (The article hadn’t included multiplication by a scalar, which of course should be there.)