16.6. Stirling Functions

Try these first

1. 1.

   What does S(1) equal in the context of Stirling functions?

   Hint

   Consider sequences with only one element.

2. 2.

   Define what recurrence relation means.

   Hint

   Think about sequences defined by previous terms.

3. 3.

   What is the value of S(1)?

   Hint

   Recall the starting point of our sequences.

4. 4.

   True or False: Initial conditions are unimportant when discussing Stirling functions.

   Hint

   Think back to how S(1) was defined.

5. 5.

   Using Stirling functions, compute S(4) and display all valid sequences, explaining why some don't count.

   Hint

   Draw out sequences and ensure each follows the rules detailed in our lessons.

6. 6.

   Can you derive a recurrence relation for a new function that counts decreasing sequences? Describe your thought process.

   Hint

   Look at how numbers relate in decay versus growth—what’s the logic reversal?