“Bateman function”的意思、由来-开放百科全书

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Bateman function

释义

Properties
References

In mathematics, the Bateman function (or k-function) is a special case of the confluent hypergeometric function studied by Harry Bateman(1931)^[1]^[2]. Bateman defined it by

Bateman discovered this function, when Theodore von Kármán asked for the solution of the following differential equation which appeared in the theory of turbulence^[3]

and Bateman found this function as one of the solutions. Bateman denoted this function as "k" function in honor of Theodore von Kármán.

This is not to be confused with another function of the same name which is used in Pharmacokinetics.

Properties

for real values of and
for if is a positive integer
If is an odd integer, then , where is the Modified Bessel function of the second kind.

References

1. ^{{Citation | last1=Bateman | first1=H. | authorlink=Harry Bateman | title=The k-function, a particular case of the confluent hypergeometric function | doi=10.2307/1989510 | mr=1501618 | year=1931 | journal=Transactions of the American Mathematical Society | issn=0002-9947 | volume=33 | issue=4 | pages=817–831}}
2. ^{{Springer|id=B/b015360|title=Bateman function}}
3. ^Martin, P. A., & Bateman, H. (2010). from Manchester to Manuscript Project. Mathematics Today, 46, 82-85. http://www.math.ust.hk/~machiang/papers_folder/http___www.ima.org.uk_mathematics_mt_april10_harry_bateman_from_manchester_to_manuscript_project.pdf

2 : Special hypergeometric functions|Special functions

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