Hans Heinrich Bürmann (died 21 June 1817, in Mannheim) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History ...

and teacher. He ran an "academy of commerce" in Mannheim since 1795 where he used to teach mathematics. He also served as a censor in Mannheim. He was nominated Headmaster of the Commerce Academy of the

Grand Duchy of Baden The Grand Duchy of Baden (german: Großherzogtum Baden) was a state in the southwest German Empire on the east bank of the Rhine. It existed between 1806 and 1918. It came into existence in the 12th century as the Margraviate of Baden and sub ...

in 1811. He did scientific research in the area of

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ap ...

and he contributed to the development of the symbolic language of mathematics. He discovered the generalized form of the

Lagrange inversion theorem In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse function of an analytic function. Statement Suppose is defined as a function of by an equa ...

. He corresponded and published with

Joseph Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaCarl Hindenburg Carl Friedrich Hindenburg (13 July 1741 – 17 March 1808) was a German mathematician born in Dresden. His work centered mostly on combinatorics and probability. Education Hindenburg did not attend school but was educated at home by a private tut ...

Iterate function composition notation

The compositional notation for the ''n''-th

iterate Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...

of function was originally introduced by Bürmann and later independently suggested by

John Frederick William Herschel Sir John Frederick William Herschel, 1st Baronet (; 7 March 1792 – 11 May 1871) was an English polymath active as a mathematician, astronomer, chemist, inventor, experimental photographer who invented the blueprint and did botanical wo ...

in 1813.

References

1817 deaths Year of birth missing 18th-century German mathematicians 19th-century German mathematicians {{germany-mathematician-stub

Iterate function composition notation

See also

References