Gustav Ferdinand Mehler, or Ferdinand Gustav Mehler (13 December 1835, in

Schönlanke Trzcianka (; german: Schönlanke) is a town in the Greater Poland region in northwestern Poland. Since 1999, it has been part of the Greater Poland Voivodeship and Czarnków-Trzcianka County. From 1975 to 1998, it was located in the Piła Voivod ...

Kingdom of Prussia The Kingdom of Prussia (german: Königreich Preußen, ) was a German kingdom that constituted the state of Prussia between 1701 and 1918.Marriott, J. A. R., and Charles Grant Robertson. ''The Evolution of Prussia, the Making of an Empire''. Re ...

– 13 July 1895, in Elbing,

German Empire The German Empire (),Herbert Tuttle wrote in September 1881 that the term "Reich" does not literally connote an empire as has been commonly assumed by English-speaking people. The term literally denotes an empire – particularly a hereditary ...

) was a German mathematician. He is credited with introducing

Mehler's formula The Mehler kernel is a complex-valued function found to be the propagator of the quantum harmonic oscillator. Mehler's formula defined a function and showed, in modernized notation, that it can be expanded in terms of Hermite polynomials (.) ba ...

; the

Mehler–Fock transform In mathematics, the Mehler–Fock transform is an integral transform introduced by and rediscovered by . It is given by :F(x) =\int_0^\infty P_(x)f(t) dt,\quad (1 \leq x \leq \infty), where ''P'' is a Legendre function In physical science an ...

; the

Mehler–Heine formula In mathematics, the Mehler–Heine formula introduced by Gustav Ferdinand Mehler and Eduard Heine describes the asymptotic behavior of the Legendre polynomials as the index tends to infinity, near the edges of the support of the weight. There are ...

; and

Mehler function In mathematics, conical functions or Mehler functions are functions which can be expressed in terms of Legendre functions of the first and second kind, P^\mu_(x) and Q^\mu_(x). The functions P^\mu_(x) were introduced by Gustav Ferdinand Mehler, in ...

s (

conical function In mathematics, conical functions or Mehler functions are functions which can be expressed in terms of Legendre functions of the first and second kind, P^\mu_(x) and Q^\mu_(x). The functions P^\mu_(x) were introduced by Gustav Ferdinand Mehler, in ...

s), in connection with his utilization of

Zonal spherical function In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group ''G'' with compact subgroup ''K'' (often a maximal compact subgroup) that arises as the matrix coefficient of a ''K''-invariant vect ...

s in Electromagnetic theory.

References

* 19th-century German mathematicians 1835 births 1895 deaths {{Germany-mathematician-stub