query: Is there a proof that the Harmonic numbers are not an elementary function?
positive_passages.docid: 10357
positive_passages.text: Do harmonic numbers have a “closed-form” expression?
negative_passages.docid: 128524
negative_passages.text: Proving there is no analytic function
negative_passages.docid: 18465
negative_passages.text: Sum and product of two transcendental numbers can't be both algebraic
negative_passages.docid: 66380
negative_passages.text: Alternating harmonic sum $\sum_{k\geq 1}\frac{(-1)^k}{k^3}H_k$
negative_passages.docid: 26353
negative_passages.text: Can any harmonic function on $\{z:0<|z|<1\}$ be extended to $z=0$?
negative_passages.docid: 80467
negative_passages.text: My proof that a harmonic series diverges..
negative_passages.docid: 47247
negative_passages.text: How do we prove the existence of uncountably many transcendental numbers?
negative_passages.docid: 1440
negative_passages.text: Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
negative_passages.docid: 27775
negative_passages.text: Proving a function is not a contraction
negative_passages.docid: 147534
negative_passages.text: The set of irrational numbers is not a $F_{\sigma}$ set.
negative_passages.docid: 139288
negative_passages.text: Formal proof that $e^x$ is not algebraic
negative_passages.docid: 109599
negative_passages.text: A finite sum involving the binomial coefficients and the harmonic numbers
negative_passages.docid: 138559
negative_passages.text: How can I show that $\frac{1}{1+|z|^2}$ isn't analytic at $z=1$?
negative_passages.docid: 14166
negative_passages.text: Hilbert space of harmonic oscillator: Countable vs uncountable?
negative_passages.docid: 151439
negative_passages.text: $\sqrt{1-x^2}$ is not a rational function
negative_passages.docid: 27933
negative_passages.text: Show that unit circle is not homeomorphic to the real line
negative_passages.docid: 129430
negative_passages.text: Hardy-Ramanujan theorem's "purely elementary reasoning"