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Nathan McKenzie's user avatar
Nathan McKenzie's user avatar
Nathan McKenzie's user avatar
Nathan McKenzie
  • Member for 12 years, 9 months
  • Last seen this week
10 votes
2 answers
1k views

Why is this sum equal to the Logarithmic Integral?

9 votes
3 answers
1k views

A general explicit formula for the generalized divisor summatory function?

7 votes
2 answers
535 views

Summing the prime power counting function up to equal some value $n$

7 votes
2 answers
217 views

Is there standard terminology to describe the not-quite-a-limit behavior of ${\tan( \log x) \over x}$ as $x$ approaches infinity?

5 votes
1 answer
190 views

Convergence of $\sum\limits_{k=0}^\infty {\binom{z}{k}} $ for complex $z$

5 votes
1 answer
189 views

Can the difference between these integrals and certain related sums be expressed in a simpler way?

5 votes
0 answers
264 views

Do the incomplete gamma functions have reflection formulas?

4 votes
1 answer
397 views

Any way to simplify integral of Confluent Hypergeometric Function of the First Kind?

4 votes
1 answer
412 views

Why do so many identities for the Logarithmic Integral begin with the terms $\log \log n + \gamma +...$?

4 votes
1 answer
446 views

Is there an explicit formula connected to $(\log\zeta(s))^2$?

3 votes
1 answer
760 views

Voronoi Summation for $d_k$ where k>2

3 votes
1 answer
54 views

Calculating the limit $\lim_{c\rightarrow 1+}\sum_{j=0}^{\lfloor\frac{\log n}{\log c}\rfloor}(-1)^j\binom{z}{j}c^j$

3 votes
1 answer
369 views

Closed form for this incomplete gamma series?

2 votes
2 answers
71 views

Concise formula for the 4D volume $x^a \cdot y^a \cdot z^b \cdot w^b \le n, where \, x,y,z,w \ge 1$?

2 votes
0 answers
189 views

Approximating sums like $\sum_{j=1}^n\sum_{k=1}^{\lfloor\frac{n}{j}\rfloor}\int_1^{\frac{n}{jk}}dx$

2 votes
1 answer
177 views

Why does this infinite sum compute the generalized binomial coefficient?

1 vote
0 answers
21 views

Simplifying $e^{-i x\log n}+e^{i x\log n}(2^{{1 \over 2}+ i x}\pi^{-{1 \over 2}+i x}\cos({\pi\over 4}-{{\pi i x}\over 2})\Gamma({1\over 2}-i x))$?

1 vote
0 answers
77 views

Can this limit be proven to converge to the Logarithmic Integral?

1 vote
0 answers
26 views

Can this transform be rewritten as a more standard integral transformation?

1 vote
0 answers
26 views

Is there a way to express a closed form for a partial derivative of this recurrence relation?

1 vote
0 answers
135 views

Deriving this recursive expression for Riemann Prime Counting Function?

0 votes
1 answer
57 views

Have the derivative of a function as a recurrence, looking for a closed form expression of the function.

0 votes
1 answer
147 views

Notation for $f(n) = \frac{\Lambda(n)}{\log n}$?

0 votes
2 answers
58 views

Can this equation be expressed in terms of tan(x) somehow?

0 votes
1 answer
19 views

Continuity of Fourier Coefficients generalized to complex values?

0 votes
0 answers
57 views

Can this nested set of integrals be evaluated?

0 votes
0 answers
196 views

Closed form for this sum involving the lower incomplete gamma function?

0 votes
0 answers
36 views

In $f(t) = \cos(\omega \cdot \log t)$, would I refer to $\omega$ as a frequency, does it have another name, or does it lack a common name?