Rising and Falling Factorials
Let represent the rising factorial and let represent the falling factorial .
Then and
For example,
Compare the third row of the table of values.
Read more about this topic: Lah Number
Famous quotes containing the words rising and, rising and/or falling:
“As wild geese that the creeping fowler eye,
Or russet-pated choughs, many in sort,
Rising and cawing at the gun’s report,
Sever themselves and madly sweep the sky—
So at his sight away his fellows fly.”
—William Shakespeare (1564–1616)
“Even Lust the Master of a hardned Face,
Blushes if thou beest in the place,
To darkness’ Curtains he retires,
In Sympathizing Night he rowls his smoaky Fires.
When, Goddess, thou liftst up thy wakened Head,
Out of the Mornings purple bed,
Thy Quire of Birds about thee play,
And all the joyful world salutes the rising day.”
—Abraham Cowley (1618–1667)
“O falling fire and piercing cry
and panic, and a weak mailed fist
clenched ignorant against the sky!”
—Elizabeth Bishop (1911–1979)