The Cunningham function, often denoted as \( C_n \), is a sequence of numbers defined as follows: - \( C_0 = 1 \) - \( C_1 = 1 \) - For \( n \geq 2 \), \( C_n = 2 \cdot C_{n-1} + C_{n-2} \) This recurrence relation means that each term is generated by taking twice the previous term and adding the term before that.

Kelvin functions, also known as cylindrical harmonics or modified Bessel functions of complex order, are special functions that arise in various problems in mathematical physics, particularly in wave propagation, heat conduction, and other areas where cylindrical symmetry is present. They are denoted as \( K_{\nu}(z) \) and \( I_{\nu}(z) \) for the Kelvin functions of the first kind and second kind, respectively.

Zonal spherical harmonics are a specific class of spherical harmonics that depend only on the polar angle (colatitude) and are independent of the azimuthal angle (longitude). They are used in various applications such as geophysics, astronomy, and climate science, often to represent functions on the surface of a sphere.

In the context of mathematics and specifically in the field of number theory, the term "Theta characteristic" often refers to a certain type of characteristic of a Riemann surface or algebraic curve that arises in the study of Abelian functions, Jacobi varieties, and the theory of divisors. 1. **Theta Functions**: Theta characteristics are closely related to theta functions, which are special functions used in various areas of mathematics, including complex analysis and algebraic geometry.

The Artin L-function is a generalization of the classical Riemann zeta function and is an important object in number theory and arithmetic geometry, particularly in the context of class field theory and algebraic number theory. It is associated with a representations of a Galois group, collections of characters, and the study of L-functions in the context of number fields. ### Definition 1.

The Beurling zeta function is a mathematical object related to number theory, specifically in the study of prime numbers. It is named after the Swedish mathematician Arne Magnus Beurling, who introduced it in the 1930s. The Beurling zeta function generalizes the classical Riemann zeta function and is used in the context of "pseudo-primes" or "generalized prime numbers.

The Clausen function, denoted as \( \text{Cl}_{2}(x) \), is a special function that is related to the integration of the sine function.

The Dirichlet L-function is a complex function that generalizes the Riemann zeta function and plays a crucial role in number theory, particularly in the study of Dirichlet characters and L-series. It is associated with a Dirichlet character \( \chi \) modulo \( k \), which is a completely multiplicative arithmetic function satisfying certain periodicity and the condition \( \chi(n) = 0 \) for \( n \) not coprime to \( k \).

An Error Correction Model (ECM) is a type of econometric model used to represent the short-term dynamics of a time series while ensuring that long-term equilibrium relationships between variables are maintained. It is particularly useful in the context of cointegrated time series data, where two or more non-stationary time series move together over time, implying a long-run equilibrium relationship between them.

Go-Back-N ARQ (Automatic Repeat reQuest) is an error control protocol used in computer networks and data communications. It is a type of sliding window protocol that allows multiple frames to be sent before needing an acknowledgment for the first frame, which increases the efficiency of data transmission. ### Key Features of Go-Back-N ARQ: 1. **Sliding Window Protocol**: The protocol utilizes a sliding window to manage the sequence of frames being sent.

Hagelbarger code refers to a specific type of error-correcting code that is used in the field of information theory and coding theory. More specifically, it is known as an example of a specific family of linear block codes. These codes are designed to detect and correct errors that may occur during the transmission of data over noisy communication channels.

Hamming code is an error-detecting and error-correcting code used in digital communications and data storage. It was developed by Richard W. Hamming in the 1950s. Hamming codes can detect and correct single-bit errors and can detect two-bit errors in the transmitted data. ### Key Features of Hamming Code: 1. **Redundancy Bits**: Hamming codes add redundant bits (also called parity bits) to the data being transmitted.

Locally testable code refers to a concept in software development and programming that emphasizes the ability to verify or "test" components of code independently and in isolation from the rest of the system. The goal of locally testable code is to ensure that individual parts of the program can be tested without requiring the entire application to be executed or without needing extensive setups or dependencies.

A Longitudinal Redundancy Check (LRC) is a type of error detection method used in digital communication and data storage to ensure the integrity of transmitted or stored data. It is particularly useful for detecting errors that may occur during data transmission over a noisy communication channel or during storage. The LRC works by calculating a checksum for each row of data, which is then combined to create a single redundancy byte that represents the overall data.

Device fingerprinting is a technique used to identify and track devices based on their unique characteristics and configurations rather than relying on traditional identifiers like cookies. It involves collecting various pieces of information about a device, such as: 1. **Browser Information**: Including the user-agent string that provides details about the browser version and operating system. 2. **Screen Resolution**: The device's screen size and resolution can be part of the fingerprint.

Maximum Likelihood Sequence Estimation (MLSE) is a method used in statistical signal processing and communications to estimate the most likely sequence of transmitted symbols or data based on received signals. It is particularly useful in environments where the signal may be distorted by noise, interference, or other factors. ### Key Concepts: 1. **Likelihood**: In statistics, the likelihood function measures the probability of the observed data given a set of parameters.

A Message Authentication Code (MAC) is a cryptographic checksum on data that provides integrity and authenticity assurances on a message. It is designed to protect both the message content from being altered and the sender's identity from being impersonated. ### Key Features of a MAC: 1. **Integrity**: A MAC helps to ensure that the message has not been altered in transit. If even a single bit of the message changes, the MAC will also change, allowing the recipient to detect the alteration.