coefficient

A coefficient ((new) lat. Coefficiens / coëfficiens , a noun of the PPA from the lat. Coefficere "participate", formed by Franciscus Vieta ), also known as an initial number or pre- number, is a number or variable added to another arithmetic expression as a factor . The coefficient can be a parameter or a key figure (physics, economics). In analysis it appears in monomials .

mathematics

In mathematics , a coefficient is a factor that belongs to a specific object such as a variable or a basis vector . Typically, objects and coefficients are indexed in the same order, so expressions like

${\displaystyle a_{1}x_{1}+a_{2}x_{2}+a_{3}x_{3}+\dotsb }$

result, with as the coefficient of the variable for each ${\displaystyle a_{n}}$ ${\displaystyle x_{n}}$ ${\displaystyle n=1,2,3,\dotsc }$

Simple example: The coefficient of the term is . ${\displaystyle 9x^{2}}$ ${\displaystyle 9}$

Examples of important mathematical coefficients:

• Coefficients of the polynomial , especially the leading coefficient
• Binomial coefficient
• Taylor coefficients (see Taylor series )
• Fourier coefficients (see Fourier series )
• Coefficients of a power series or Laurent series , here in particular the residual
• Clebsch-Gordan coefficient

See also : parameters (math)

physics

In physics , a coefficient is often, but not always, a quantity in the dimension number that describes a property of certain materials, bodies or systems. In older technical literature, coefficients are also called coefficients . Examples:

• Static friction coefficient , sliding friction coefficient
• Drag coefficient (" C _w value")
• Heat transfer coefficient

Far from every physical constant of the dimension number is called a coefficient. Counterexamples:

• Fundamental natural constants such as the fine structure constant
• Ratios from similarity laws such as the Reynolds number

Examples of dimensional coefficients:

• Coefficient of thermal expansion
• Doppler coefficient
• Coolant loss coefficient

chemistry

Stoichiometry

In stoichiometry , the stoichiometric coefficient indicates in a reaction equation how many particles or moles of a substance react with how many particles or moles of other substances. If the coefficient is 1, it is omitted.

Example ( oxyhydrogen reaction ):

${\displaystyle \mathrm {2\ H_{2}+O_{2}\longrightarrow 2\ H_{2}O} }$

Hydrogen and water have the stoichiometric coefficient 2 because

• 2 hydrogen molecules react with one oxygen molecule to form 2 water molecules
• 2 moles of hydrogen react with one mole of oxygen to form 2 moles of water.

Physical chemistry and biochemistry

• Binding coefficient (synonym coefficient of preferential interaction , English preferential interaction coefficient)

Sports

In sporting associations such. B. UEFA also has coefficients which clubs or teams rate based on their previous successes.

Economics

• The Gini coefficient is a measure of inequality.
• The total requirement coefficient is a quantity for resource use planning.