Puck is one of the natural satellites of Uranus. It was discovered in 1985 by the Voyager 2 spacecraft during its flyby of the planet. Puck is the second-largest of Uranus' inner moons and is named after a character from William Shakespeare's play "A Midsummer Night's Dream." Puck has a somewhat irregular shape, measuring approximately 162 kilometers (around 100 miles) in diameter.

Thiazzi is not a widely recognized term related to celestial bodies or moons in the scientific community as of my last update. It is possible that it might refer to a fictional moon, a lesser-known astronomical object, or a recent discovery that has not gained significant attention.

Margaret, also known as Neptune IX, is one of the moons of the planet Neptune. It was discovered in 1989 by a team of astronomers using data from the Voyager 2 spacecraft. Margaret is one of the smaller moons orbiting Neptune and is classified as an irregular moon, meaning it has a more eccentric and inclined orbit compared to the larger, more geologically active moons.

As of my last knowledge update in October 2023, Lucien Poirier could refer to different subjects depending on the context. It's important to clarify the context to provide accurate information. 1. **Historical Figure**: Lucien Poirier was a notable French figure perhaps known for contributions in a specific field, but more context would be needed to identify his contributions accurately.

A "death ray" is a term that has been used in various contexts to describe a hypothetical or fictional weapon capable of causing death or destruction over long distances, typically through the application of concentrated energy or radiation. The concept has appeared in science fiction literature, movies, and even in the early visions of future technology. Historically, figures like Nikola Tesla and H.G. Wells have popularized the idea of a death ray.

Homomorphism density is a concept from combinatorics and graph theory that deals with the frequency of the occurrence of one graph within another graph. More formally, it relates to the density of homomorphisms from one graph to another.

Gamma and related functions are a family of special functions in mathematics that extend the concept of factorials to non-integer values. ### Gamma Function (Γ) The **Gamma function**, denoted as \( \Gamma(n) \), is defined for all complex numbers except the non-positive integers and can be thought of as a continuous extension of the factorial function. Specifically, for any positive integer \( n \), \[ \Gamma(n) = (n-1)!

Bernoulli's triangle is a mathematical construct related to the binomial coefficients, similar to Pascal's triangle. The elements of Bernoulli's triangle are known as Bernoulli numbers, which are a sequence of rational numbers that have important applications in number theory, analysis, and combinatorics.

The **binomial approximation** refers to several mathematical ideas involving binomial expressions and the binomial theorem. Most commonly, it is used in the context of approximating probabilities and simplifying calculations involving binomial distributions or binomial coefficients.

The Binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent Bernoulli trials (experiments with two possible outcomes, often termed "success" and "failure"). This type of distribution is particularly useful in situations where you want to determine the likelihood of a certain number of successes within a series of trials.

The binomial series is a way to express the expansion of a binomial expression raised to a power. Specifically, it provides the expansion of the expression \((a + b)^n\) for any real (or complex) number \(n\).

The Extended Negative Binomial Distribution, sometimes referred to in some contexts as the Generalized Negative Binomial Distribution, is a statistical distribution that generalizes the standard negative binomial distribution. The standard negative binomial distribution typically models the number of failures before a specified number of successes occurs in a sequence of independent Bernoulli trials.

Falling and rising factorials are two mathematical concepts often used in combinatorics and algebra to describe specific products of sequences of numbers. They are particularly useful in the context of permutations, combinations, and polynomial expansions. Here's an overview of both: ### Falling Factorials The falling factorial, denoted as \( (n)_k \), is defined as the product of \( k \) consecutive decreasing integers starting from \( n \).

The term "fibonomial coefficient" refers to a mathematical concept that combines elements from both Fibonacci numbers and binomial coefficients. It is defined in relation to the Fibonacci sequence, which is a series of numbers where each number (after the first two) is the sum of the two preceding ones. The fibonomial coefficient is typically denoted as \( \binom{n}{k}_F \) and is defined using Fibonacci numbers \( F_n \).

The generalized hypergeometric function, denoted as \(_pF_q\), is a special function defined by a power series that generalizes the hypergeometric function.

The pseudogamma function is a mathematical function that generalizes the concept of the gamma function. While the traditional gamma function, denoted as \(\Gamma(z)\), is defined for complex numbers with a positive real part, the pseudogamma function can be used in a wider context, particularly in the field of number theory and special functions. One common interpretation of the pseudogamma function is based on the notion of providing alternatives or approximations to the gamma function.

The Sierpiński triangle, also known as the Sierpiński gasket or Sierpiński sieve, is a fractal and attractive fixed set with an overall shape that resembles an equilateral triangle. It is constructed through a recursive process that involves removing smaller triangles from a larger triangle. Here’s how it is usually created: 1. **Start with an equilateral triangle**: Begin with a solid equilateral triangle.