03/01/2020, 10:47 PM

http://mathworld.wolfram.com/GeneratingFunction.html

in a simple sequence, example the fib sequence we have

https://en.wikipedia.org/wiki/Fibonacci_number

x²-x-1 = 0

evalueting the generating function with a number, example 10

f(10) = 10² - 10 - 1 = 89

with the power sum of the fib multiplied by 10 one get the reciprocal of 89

other sequences

https://en.wikipedia.org/wiki/Hofstadter_sequence

http://mathworld.wolfram.com/MallowsSequence.html

https://en.wikipedia.org/wiki/Umbral_calculus

https://en.wikipedia.org/wiki/1_%2B_2_%2..._summation

Would be possible do some umbral calculus with tetration indexes and series with recurrence inside recurrence ?

in a simple sequence, example the fib sequence we have

https://en.wikipedia.org/wiki/Fibonacci_number

x²-x-1 = 0

evalueting the generating function with a number, example 10

f(10) = 10² - 10 - 1 = 89

with the power sum of the fib multiplied by 10 one get the reciprocal of 89

other sequences

https://en.wikipedia.org/wiki/Hofstadter_sequence

http://mathworld.wolfram.com/MallowsSequence.html

https://en.wikipedia.org/wiki/Umbral_calculus

https://en.wikipedia.org/wiki/1_%2B_2_%2..._summation

Would be possible do some umbral calculus with tetration indexes and series with recurrence inside recurrence ?