olemus
funktsioonide või konstantide sarja matemaatiline funktsioon, mille esitamisel lõpmatu reana on need funktsioonid või konstandid selle rea kordajad;
näide: funktsioon (1 - 2ux + u²)^-1/2 on Legendre'i polünoomide P_n(x) genereeriv funktsioon, sest ta reaksarendusel on kuju

= of a given series of functions or constants, a mathematical function that, when represented by an infinite series, has those functions or constants as coefficients in the series
Example: the function (1 - 2ux + u²)^-1/2 is a generating function of the Legendre polynomials P_n(x) by virtue of the expansion

02.04.06
generating function
Of a given series of functions or constants, a mathematical function that, when represented by an infinite series, has those functions or constants as coefficients in the series.
Example: The function (1 - 2ux + u2)-1/2 is a generating function of the Legendre polynomials Pn(x) by virtue of the expansion

ülevaateid
http://willperkins.org/6221/slides/generating.pdf

https://en.wikipedia.org/wiki/Generating_function

https://www.math.cmu.edu/~af1p/Teaching/Combinatorics/Slides/Generating-Functions.pdf

https://www.math.cmu.edu/~lohp/docs/math/2011-228/mit-ocw-generating-func.pdf

https://www2.math.upenn.edu/~wilf/gfologyLinked2.pdf