# Questions tagged [quantum-calculus]

Quantum calculus encompasses $q$-calculus and $h$-calculus, and is a notion of "calculus without limits". Do not confuse with the (quantum-mechanics) tag. For questions on Schrodinger's equation and solutions, use (quantum-mechanices), (pde), (fourier-analysis), and/or (calculus) as appropriate.

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### Combinatorics - Q Calculus Pascal's Identity Proof

I have been trying to get started on this simple combinatorics proof. This has led me to start a proof by induction using pascal's identity from https://en.wikipedia.org/wiki/...
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### Quantum Calculus Prove Q Binomial Coefficient Analogue

Parts a and b are trivial so those are of no concern. My conclusion for part c is that a proper q analog is the q binomial coefficient, counting the number of subspaces of dimension k in a vector ...
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### Bound for deformed binomial coefficients

Let $\mu$ be a positive real number smaller than $1$. Define $${k\choose{r}}_{\mu}=\frac{\prod_{i=1}^{k}(1-\mu^{2i})}{\prod_{i=1}^{k-r} (1-\mu^{2i}) \prod_{i=1}^{r} (1-\mu^{2i})}$$ Then I need to show ...
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### Why is $q$ sometimes a complex number, but other times a prime power?

In the fields of representation theory and quantum algebra, we often start with some $\mathbf{C}$-algebra and study it's quantization as an algebra over $\mathbf{C}(q)$, using the algebra structure to ...
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### Studying quantized algebras, what motivates the choice of base ring?

In the fields of representation theory and quantum algebra, we often start with, for example, some $\mathbf{C}$-algebra $A$ and study a quantization of $A$ by adjoining an indeterminate $q$, or ...
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1 vote
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### Studying quantized algebras, why introduce $q^{1/2}$ instead of just $q$?

In the fields of representation theory and quantum algebra, we often study quantized versions of algebraic objects by regarding them as algebras over $\mathbf{C}(q)$, or some subring of $\mathbf{C}(q)$...
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### Connection between the quantum calculus and fractional calculus developed by Riemann-Liouvelle, Caputo and others?

I wonder are there any connection between the quantum calculus and fractional calculus developed by Riemann-Liouvelle, Caputo and others?
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1 vote
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### What does the statement "x is a diagram of classical logics" mean?

From the Wikipedia entry on quantum logic A more modern approach to the structure of quantum logic is to assume that it is a diagram – in the sense of category theory – of classical logics (see ...
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### double integrals on quantum calculus

I need references or book recommendations to find properties of double integrals on quantum calculus. Especially i need analogue of Fubini's theorem on q-calculus.
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### improper integrals in q-calculus

In quantum calculus is this equality possible for improper integrals? $\lim_{x\to\infty}\int_0^xf(t)d_qt=\int_0^\infty f(x)d_qx$
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### Ejemplos de la integral de Jackson (Examples of Jackson's Integral)

Original question in Spanish La integral de Jackson está definida en el cálculo cuántico, y quisiera que alguien me ayudara a la explicación de un ejemplo de este estilo de integrales. Gracias Added ...
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