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The riddle does not exist. If a question can be put at all, then it can also be answered.

Wittgenstein, Ludwig


May
13
comment Umbral calculus with negative indices (and powers)
@Did It does not, hence my comments. Half the bounty value was automatically awarded to the top voted answer.
May
12
comment Treating indices as if they were exponents
@MattGroff I do not want to find a series. I want to use some umbral-like linear functional to interpret $a^n$ as $a_n$, which is analogous to (35) in this MathWorld article.
May
11
comment Treating indices as if they were exponents
@MattGroff See also this.
May
11
comment Treating indices as if they were exponents
@MattGroff I want to do something analogous to (35) in this MathWorld article.
May
11
revised Treating indices as if they were exponents
added 2 characters in body
May
11
comment Treating indices as if they were exponents
@Sh3ljohn Does the question make sense now?
May
11
comment Treating indices as if they were exponents
@Did What is NARQ?
May
11
revised Treating indices as if they were exponents
added 100 characters in body
May
11
revised Treating indices as if they were exponents
added 100 characters in body
May
11
revised Treating indices as if they were exponents
added 100 characters in body
May
11
comment Treating indices as if they were exponents
@ChrisEagle Umbral calculus (see Roman; p. 96)
May
11
asked Treating indices as if they were exponents
May
8
awarded  Caucus
May
6
comment Showing $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$ using complex integration
@aziiri Recall that $e^{iz} = \cos z + i\sin z$ and use the Squeeze Theorem.
May
2
comment Umbral calculus with negative indices (and powers)
Can you elaborate?
May
2
comment Umbral calculus with negative indices (and powers)
I also think that if $a_{−1}, a_{−2}, a_{-3}, \ldots$ is our infinite sequence, then if we insist on using nonnegative integers we let $\{a_{-n}\}_{n \in \mathbb N} = \{b_{n - 1}\}_{n \in \mathbb N}$. But it seems unconventional and I could not find any articles or books that discuss this. Can you justify it rigorously so that I can give you 50 rep?
Apr
27
comment Integral of a floor function
Graph $f(x)$ and calculate the area of each rectangle.
Apr
26
revised Umbral calculus with negative indices (and powers)
edited tags
Apr
24
asked Umbral calculus with negative indices (and powers)
Apr
24
revised The geometric mean of primes less than or equal to $x$
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