local
(0.000 seconds)
1—10 of 217 matching pages
1: 31.3 Basic Solutions
…
►
denotes the solution of (31.2.1) that corresponds to the exponent at and assumes the value there.
If the other exponent is not a positive integer, that is, if , then from §2.7(i) it follows that exists, is analytic in the disk , and has the Maclaurin expansion
…
►Solutions (31.3.1) and (31.3.5)–(31.3.11) comprise a set of 8 local solutions of (31.2.1): 2 per singular point.
…For example, is equal to
…
►The full set of 192 local solutions of (31.2.1), equivalent in 8 sets of 24, resembles Kummer’s set of 24 local solutions of the hypergeometric equation, which are equivalent in 4 sets of 6 solutions (§15.10(ii)); see Maier (2007).
2: 31.7 Relations to Other Functions
…
►
31.7.1
►Other reductions of to a , with at least one free parameter, exist iff the pair takes one of a finite number of values, where .
…
►
31.7.2
►
31.7.3
►
31.7.4
…
3: 4.42 Solution of Triangles
…
4: 31.5 Solutions Analytic at Three Singularities: Heun Polynomials
…
►
31.5.2
…
5: 31.1 Special Notation
…
►The main functions treated in this chapter are , , , and the polynomial .
…
6: 31.9 Orthogonality
7: 37.20 Mathematical Applications
…
►For regular domains, such as square, sphere, ball, simplex, and conic domains, they are used to study convolution structure, maximal functions, and interpolation spaces, as well as localized kernel and localized frames.
…
8: 2.6 Distributional Methods
…
►Let be locally integrable on .
The Stieltjes
transform of is defined by
…Since is locally integrable on , it defines a distribution by
…
►In terms of the convolution product
…of two locally integrable functions on , (2.6.33) can be written
…
9: 28.19 Expansions in Series of Functions
10: 33.11 Asymptotic Expansions for Large
…