 About 4,500 results  books.google.com We introduce the notation, also called Kummer's function or the Mfunction N " (a,
n)zn satisfying iF1(a;7;0) = l and Kummer's differential equation for u(z) = \Fi{a;j;z)
is zu"{z) + (7 z)m'(z)  au{z) = 0 which is obtained by taking the limit b — > 00 in ... 

 books.google.com the Bessel differential equation z2f + zf + ( z2 − ν2 ) f = 0, (2.17) • the Legendre
differential equation ( 1−z2 ) f−2zf+ν(ν+1)f=0, (2.18) • the confluent
hypergeometric (Kummer) differential equation zf+ (c−z)f −af= 0, (2.19) • the
Whittaker differential ... 

 books.google.com ... isadegenerate form of ahypergeometric differential equation where twoof the
three regularsingularities mergeintoan irregular singularity. There are several
common standard forms of confluent hypergeometric functions: •Kummer's (
confluent ... 

 books.google.com ... into an irregular singularity. There are several co standard forms of confluent
hypergeometric functions: Kummer's (confluent hypergeometric) function M(a,b,z
), introduced Kummer (1837), is a solution to Kummer's differential equation. 

 books.google.com Our two equations then become P Vr + C(2s + 1)  p] ~  (s  A)fx = 0. (8.181) ^4 + [
(25 + l)p]^ dp dp and p^4 + [(2s + 1)  p] AA _ (s _ ^ + l)/2 = 0. (8.182) dpz dp
These two equations are known as special examples of Kummer's differential ... 

 books.google.com Using the Hermite polynomials as examples, consider the following: (a)
Transform the Hermite equation into ... a moment that the Hermite differential
equation is a special case of the confluent hypergeometric or Kummer's
differential equation: ... 

 books.google.com Equation (41) or (42) has a regular singularity at z I 0 and an irregular singularity
at z I 00, which is formed by the ... Consequently, (41) or (42) is called the
confluent hypergeometric equation or Kummer's differential equation after Ernst
Eduard ... 

 books.google.com For the case when )1 : O the general solution of this differential equation takes
the form, for c G (O, oo), as 1 where the ... Kummer equation The Kummer
differential equation is a special case of the confluent hypergeometric differential
... 

 books.google.com 2 _0 dkz dk dk3 dk k  k3 i  13 dk _ (Jacobi's equation 12) This equation, which
may be called J acobi's differential equation for the moduli, was one of the targets
of Kummer's work. It has, among its particular integrals, the quotients of solutions
... 

 books.google.com The hypergeometric differential equation (4.2) has a regular singularity at infinity.
The point at infinity is not a regular singularity for Kummer's differential equation (
4.5). 4.2.3. The Solution Near a Regular Point Let 2 = 0 be a regular point of the ... 

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