Euler Reflection Formula
The above MZVs satisfy the Euler reflection formula:
- for
Using the shuffle relations, it is easy to prove that:
- for
This function can be seen as a generalization of the reflection formulas.
Read more about this topic: Multiple Zeta Function
Famous quotes containing the words reflection and/or formula:
“Public morning diversions were the last dissipating habit she obtained; but when that was accomplished, her time was squandered away, the power of reflection was lost, [and] her ideas were all centered in dress, drums, routs, operas, masquerades, and every kind of public diversion. Visionary schemes of pleasure were continually present to her imagination, and her brain was whirled about by such a dizziness that she might properly be said to labor under the distemper called the vertigo.”
—Sarah Fielding (1710–1768)
“But suppose, asks the student of the professor, we follow all your structural rules for writing, what about that “something else” that brings the book alive? What is the formula for that? The formula for that is not included in the curriculum.”
—Fannie Hurst (1889–1968)