Multiply integers of the same parity as n while stepping downward by two. The result panel keeps double factorial and its numerical trail together.
Double factorials occur in sphere formulas, repeated derivatives, Gaussian moments, combinatorial matchings, and trigonometric integrals.
The double factorial n!! multiplies n, n−2, n−4, and so on, ending at one for odd n or two for positive even n. Both 0!! and 1!! equal one.
In double factorial, the relationship among the quantities matters just as much as their arithmetic.
For n=9, 9!!=9·7·5·3·1=945. For comparison, 9! includes the even factors too and equals 362,880.
Two exclamation marks describe a step of two, not applying factorial twice. Parity determines the terminal factor and must remain visible in hand work.
Keep any applicable units beside the source values; the browser cannot detect a silent mismatch during double factorial.
Write the descending sequence with difference two, verify that every factor has the same parity as n, and multiply the factors exactly. Double Factorial also leads to ordinary factorial.
Before entering nonnegative integer n, identify what each field represents. Its label determines how the double factorial relationship interprets the entry. The browser cannot supply missing unit context, so preserve that context in your notes.
Increasing n by two multiplies the result by the new n; increasing by one switches parity and creates a different sequence. That behavior gives the double factorial output a built-in reasonableness test.
Ordinary factorial uses every intervening integer and therefore grows faster at comparable inputs. Writing “Double factorial” beside the output prevents that mix-up.
A final answer should carry enough context to be reusable: name it double factorial, attach any applicable unit, and record the rounding point. If another person must reproduce the result, the supplied input in the field and the displayed formula are more informative than the decimal alone.
A useful note for this result contains the supplied inputs (nonnegative integer n), the answer label, and the chosen precision. That record can be checked without recreating the entire page state.
The number from Double Factorial is incomplete without its convention. Record the roles Nonnegative integer n, together with whether positions are distinguishable, events may overlap, or trials are replaced. Those facts define the sample space and cannot be recovered reliably from a copied result alone.
For Double Factorial, use a boundary case such as zero events, one object, certainty, or impossibility when it belongs to the model. A correct boundary result is a useful defense against an unnoticed indexing or probability-scale error.
No.
It is 1.
At 2.
At 1.