Christian Kramp (8 July 1760 – 13 May 1826) was a French mathematician, who worked primarily with

factorial In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \t ...

s. $Kramp, Christian – Analyse des réfractions astronomiques et terrestres, 1799 – BEIC 745581$ Christian Kramp's father was his teacher at grammar school in

Strasbourg Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Alsatian, Strossburi , gsw, label=Haut Rhin Alsatian, Strossburig ) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the Eu ...

. Kramp studied medicine and graduated; however, his interests certainly ranged outside medicine, for in addition to a number of medical publications he published a work on

crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...

in 1793. In 1795, France annexed the

Rhineland The Rhineland (german: Rheinland; french: Rhénanie; nl, Rijnland; ksh, Rhingland; Latinised name: ''Rhenania'') is a loosely defined area of Western Germany along the Rhine, chiefly its middle section. Term Historically, the Rhinelands ...

area in which Kramp was carrying out his work and after this he became a teacher at

Cologne Cologne ( ; german: Köln ; ksh, Kölle ) is the largest city of the German western States of Germany, state of North Rhine-Westphalia (NRW) and the List of cities in Germany by population, fourth-most populous city of Germany with 1.1 m ...

(this city was French from 1794 to 1815), teaching mathematics,

chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

, and

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

. Kramp could read and write in German and French. Kramp was appointed professor of mathematics at

, the town of his birth, in 1809. He was elected to the geometry section of the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

in 1817. As Bessel, Legendre and

Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

did, Kramp worked on the generalised factorial function which applied to non-

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

s. His work on factorials is independent of that of James Stirling and Vandermonde. He was the first to use the notation ''n''! (''Elements d'arithmétique universelle'', 1808). In fact, the more general concept of factorial was found at the same time by Arbogast. ''Kramp's function'', a scaled

complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...

error function In mathematics, the error function (also called the Gauss error function), often denoted by , is a complex function of a complex variable defined as: :\operatorname z = \frac\int_0^z e^\,\mathrm dt. This integral is a special (non-elementary ...

, is today better known as the

Faddeeva function The Faddeeva function or Kramp function is a scaled complex complementary error function, :w(z):=e^\operatorname(-iz) = \operatorname(-iz) =e^\left(1+\frac\int_0^z e^\textt\right). It is related to the Fresnel integral, to Dawson's integral, a ...

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* 1760 births 1826 deaths 18th-century French mathematicians 19th-century French mathematicians French people of German descent Members of the French Academy of Sciences {{France-mathematician-stub