HSC 2016 MX2 Integration Marathon (archive) (3 Viewers)

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leehuan

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Re: MX2 2016 Integration Marathon

Requires multi-valued gamma function with one real and one imaginary argument, according to Mathematica. So a reduction formula definitely exists.
I'll let it sit there then.

 

glittergal96

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Re: MX2 2016 Integration Marathon

Actually, I just realised, nth root of x is irreducible, so there is no reduction formula, only a general form.


where .

(Consider only the non-negative reals to avoid having to talk about multivalued things.)


This latter integral clearly gives us an integration by parts reduction formula (dropping exponent by two each time). Then it's just a matter of changing the variables back to x to get a reduction formula for the original integral.


Someone else can fill in the details if they like.
 

Paradoxica

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Re: MX2 2016 Integration Marathon



where .

(Consider only the non-negative reals to avoid having to talk about multivalued things.)


This latter integral clearly gives us an integration by parts reduction formula (dropping exponent by two each time). Then it's just a matter of changing the variables back to x to get a reduction formula for the original integral.


Someone else can fill in the details if they like.
Yes, but in order for a reduction formula to exist, we have to make the "n" which the y-substitution depends on independent to the "n" which the reduction formula depends on.
 

glittergal96

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Re: MX2 2016 Integration Marathon

Yes, but in order for a reduction formula to exist, we have to make the "n" which the y-substitution depends on independent to the "n" which the reduction formula depends on.
Ah of course, silly me. :).
 

KX

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Re: MX2 2016 Integration Marathon

lol why are you using your alt?
 

seanieg89

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Re: MX2 2016 Integration Marathon

lol why are you using your alt?
Was in my office and knew my alt password off the top of my head, but would have needed to check one of those password reset emails to get my password for the main acct.
 
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