exponential generating function造句
例句與造句
- Similar asymptotic analysis is possible for exponential generating functions.
- This umbral exponential thus amounts to the exponential generating function of the Pochhammer symbols.
- Manipulations of these functions are done in essentially the same way as for the exponential generating functions.
- Exponential generating functions are generally more convenient than ordinary generating functions for combinatorial enumeration problems that involve labelled objects.
- The relations corresponding to other operations depend on whether we are talking about labelled or unlabelled structures ( and ordinary or exponential generating functions ).
- It's difficult to find exponential generating function in a sentence. 用exponential generating function造句挺難的
- There are two types of generating functions commonly used in symbolic combinatorics ordinary generating functions, used for combinatorial classes of unlabelled objects, and exponential generating functions, used for classes of labelled objects.
- In the labelled case we use an exponential generating function ( EGF ) " g " ( " z " ) of the objects and apply the Labelled enumeration theorem, which says that the EGF of the configurations is given by
- Once more, start with the exponential generating function g ( z, u ), this time of the class \ mathcal { P } of permutations according to size where cycles of length more than n / 2 are marked with the variable u:
- An alternative method for deriving the same generating function uses the recurrence relation for the Bell numbers in terms of binomial coefficients to show that the exponential generating function satisfies the differential equation B'( x ) = e ^ { x } B ( x ).
- The notation of brackets and braces, in analogy to binomial coefficients, was introduced in 1935 by Jovan Karamata and promoted later by Donald Knuth . ( The bracket notation conflicts with a common notation for Gaussian coefficients . ) The mathematical motivation for this type of notation, as well as additional Stirling number formulae, may be found on the page for Stirling numbers and exponential generating functions.
- :I think the revised version of the article is substantially better, because it explains right away why the Bernoulli numbers are of interest and why they were studied . ( They are coefficients of the closed form of sum ( " i n " ) for various " n " . ) The older version of the article starts of by saying they were named after Jakob Bernoulli by Abraham de Moivre ( which is not particularly important ) and then follows with a definition of the numbers via an exponential generating function.
- How does one efficiently figure out which function is given by, say, f ( x ) = \ sum _ { n = 0 } ^ \ infty \ frac { n ^ 2 x ^ n } { n ! } ? ( In other words, how do we find the exponential generating function for the sequence { n 2 } ? ) I know which function it is, because I've worked it out a couple of different ways ( including finding it in a list ), but I feel that I'm missing the easy way to calculate it.