mmcdara

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How can we obtain the expression of the function f : R --> R defined, for each (a, b) such that -oo < a <= b < +oo, by this equality?

Int(f(x), x=a..b) = Int(f(x), x=1/b..1/a)

Replacing x by 1/y in the rhs integral shows that f satisfies this functional equation 

f(y) = f(1/y)/y^2

(note this impose y <> 0, see the PS below)
Functional equations is not y cup of tea and Maple (2015) doesn't seem to have any feature to solve them.
Could anyone explain me how f can be obtained?

PS:
I inadvertently obtained this equality between integrals as I was comparing the performances of different numerical integration methods.
One of the functions in my benchmarks suite had the expression f(x)=1/(1+x^2)... and I "discovered", by changing x to 1/y to ease the numerical integration, that f checked the inequality of the first code snippet.
Thus , for any constant C, C*f  is a solution of the functional equation.
Note that f(x) being strictly positive, 1/y > 0 and the functional equation is always defined.

Hi,

Is it possible to capture programatically the values of theta, phi and psi when you manually rotate a 3D plot?

Thanks in advance

PS: The target version is Maple 2020

Hi, 
The result below surprises me.
Why does  rgf_findrecur return a result instead of saying that there is no homogeneous linear recurrence of order 1?

interface(version)

Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895


genfunc:-rgf_findrecur(1, [1, 2, 3, 4], t, n);
                       t(n) = 2 t(n - 1)

PS: maybe this was a problem in Maple 2015, if it has been corrected since just let me know


 

 

Hi, 

This is the context                                                                                             
A mathematical expression f has been coded by a two stage process of the form 

(u and s are character strings)
I do not know what f is, but I know what P1, P2 are and I know s too. 
I would like to recover f.

Here is the particular couple of coding processes that I consider

f := sqrt(x);    # assumed to be unknown

u  := sprintf("%Zm", f);                     # "process" P1
s  := StringTools:-Encode(u,':-base64');     # "process" P2

# The "inverse" of P2 is
v := StringTools:-Decode( s, 'encoding' = ':-base64' );

# Does it exist an operation to recover f from v?


Thanks in advance

 

Hi,
I see more and more contributions where the content of the mw file is replaced by a code snippet and, possibly, an image as illustration.
Do we have to consider this as the new norm to post question and to submit replies or answers?

(this question is related to the one Carl Love posted a few days ago  Why can't I display any worksheet? and which, if I'm not mistaken, has not been definively answered)

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