mjhjmtu

I would like to define an operator rsum which has all the same functionality of sum with the only difference being that rsum displays a mirrored image of the sigma glyph.

I have found the following questions which each address a part of what I want:

How are big operators defined?

Reversed letters in a mathematical formula

However, I'm having difficulty in marrying the two accepted answers into a single solution. How would I go about accomplishing this? (An answer to this question doesn't necessarily have to use the approaches in the other questions.)

I don't anticipate using custom fonts for this purpose, but the capability to do so wouldn't be unappreciated (if not by me by someone in the future, I'm sure).

Well, it's almost automatic. ;-)

documentclassarticle
usepackageamsmath
usepackagegraphicx

makeatletter
newcommandrsumDOTSBrsum@slimits@
newcommandrsum@mathopmathpalettersum@@relax
newcommandrsum@@[2]reflectbox$m@th#1sum@$
makeatother

begindocument

[
sum_i=1^nrsum_i=1^n
qquad
textstyle
sum_i=1^nrsum_i=1^n
]

enddocument

The main idea is to reflect the symbol in the appropriate math style; some bells and whistles for amsmath have been added.

Should you need also rotated versions, here they are:

documentclassarticle
usepackageamsmath
usepackagegraphicx

makeatletter
newcommandrsumDOTSBrsum@slimits@
newcommandrsum@mathopmathpalettersum@@relax
newcommandrsum@@[2]reflectbox$m@th#1sum@$

newcommandusumDOTSBusum@slimits@
newcommandusum@mathopmathpaletteudsum@@90
newcommanddsumDOTSBdsum@slimits@
newcommanddsum@mathopmathpaletteudsum@@-90
newcommandudsum@@[2]%
 vcenter%
 sboxz@$m@th#1sum@$%
 hbox to wdz@%
 hss
 resizeboxifxdisplaystyle#1else0.9fiwdz@dimexprhtz@%
 rotatebox[origin=c]#2$m@th#1sum@$%
 %
 hss
 %
 %

makeatother

begindocument

[
sum_i=1^nrsum_i=1^n
qquad
textstyle
sum_i=1^nrsum_i=1^n
]

[
sum_i=1^nusum_i=1^n
qquad
textstyle
sum_i=1^nusum_i=1^n
]

[
sum_i=1^ndsum_i=1^n
qquad
textstyle
sum_i=1^ndsum_i=1^n
]

enddocument