# of one variable

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## 11—20 of 298 matching pages

##### 11: 1.10 Functions of a Complex Variable

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###### §1.10(i) Taylor’s Theorem for Complex Variables

… ►Analytic continuation is a powerful aid in establishing transformations or functional equations for complex variables, because it enables the problem to be reduced to: (a) deriving the transformation (or functional equation) with real variables; followed by (b) finding the domain on which the transformed function is analytic. …##### 12: 19.16 Definitions

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►When one variable is 0 without destroying convergence, any one of (19.16.14)–(19.16.17) is said to be

*complete*and can be written as an $R$-function with one less variable: …##### 13: Bibliography F

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The third Appell function for one large variable.
J. Approx. Theory 165, pp. 60–69.
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The second Appell function for one large variable.
Mediterr. J. Math. 10 (4), pp. 1853–1865.
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##### 14: 10.73 Physical Applications

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►and on separation of variables we obtain solutions of the form ${\mathrm{e}}^{\pm \mathrm{i}n\varphi}{\mathrm{e}}^{\pm \kappa z}{J}_{n}\left(\kappa r\right)$, from which a solution satisfying prescribed boundary conditions may be constructed.
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►On separation of variables into cylindrical coordinates, the Bessel functions ${J}_{n}\left(x\right)$, and modified Bessel functions ${I}_{n}\left(x\right)$ and ${K}_{n}\left(x\right)$, all appear.
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##### 15: Annie A. M. Cuyt

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►A lot of her research has been devoted to rational approximations, in one as well as in many variables, and sparse interpolation.
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##### 16: Bibliography Y

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Generalized Hypergeometric Functions and Laguerre Polynomials in Two Variables.
In Hypergeometric Functions on Domains of Positivity, Jack
Polynomials, and Applications (Tampa, FL, 1991),
Contemporary Mathematics, Vol. 138, pp. 239–259.
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##### 17: 18.2 General Orthogonal Polynomials

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►It is assumed throughout this chapter that for each polynomial ${p}_{n}(x)$ that is orthogonal on an open interval $(a,b)$ the variable
$x$ is confined to the closure of $(a,b)$

*unless indicated otherwise.*(However, under appropriate conditions almost all equations given in the chapter can be continued analytically to various complex values of the variables.) …##### 18: Mathematical Introduction

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►Special functions with one real variable are depicted graphically with conventional two-dimensional (2D) line graphs.
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