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11: Mathematical Introduction

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$ℂ$	complex plane (excluding infinity).
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empty sums	zero.
empty products	unity.
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12: Preface

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Bille C. Carlson, Iowa State University

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13: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions

… ►(The empty set is considered to have one permutation consisting of no cycles.) …

14: 18.39 Applications in the Physical Sciences

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§18.39(iii) Non Classical Weight Functions of Utility in DVR Method in the Physical Sciences

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15: 1.4 Calculus of One Variable

… ►The utility of the generalization implicit in the Stieltjes measure appears when $\alpha (x)$ is not everywhere continuous, but has discontinuous jumps at specific values of $x$, say $x_n\in (a,b)$. …

16: Bibliography

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SPHEREPACK 2.0: A Model Development Facility. NCAR Technical Note Technical Report TN-436-STR, National Center for Atmospheric Research.

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Notes:

SPHEREPACK 2.0 is a collection of Fortran programs that facilitates computer modeling of geophysical processes. Accurate solutions are obtained via the spectral method that uses both scalar and vector spherical harmonic transforms. The package also contains utility programs for computing the associated Legendre functions. SPHEREPACK 3.1 was released in August 2003.

External Links:

FullText, SPHEREPACK 3.1

Referenced by:

1st item.

Encodings:

BibTeX

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17: Bibliography C

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Orthogonalization Procedures and the Localization of Wannier Functions. Phys. Rev. 105, pp. 102–103.

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External Links:

Document, Link, ZentralBlatt

Referenced by:

Profile Bille C. Carlson.

Encodings:

BibTeX

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Eigenvalues of Density Matrices. Phys. Rev. 121, pp. 659–661.

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External Links:

Document, Link, ZentralBlatt

Referenced by:

Profile Bille C. Carlson.

Encodings:

BibTeX

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Lauricella’s hypergeometric function $F_D$ . J. Math. Anal. Appl. 7 (3), pp. 452–470.

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External Links:

Document, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§19.15, §19.16(iii), §19.18(ii), §19.25(vii), §19.28, §19.28, Profile Bille C. Carlson.

Encodings:

BibTeX

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Symmetry in c, d, n of Jacobian elliptic functions. J. Math. Anal. Appl. 299 (1), pp. 242–253.

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External Links:

ISSN 0022-247X, Document, MathReview Entry, ZentralBlatt

Referenced by:

§19.25(v), §19.25(v), §22.13(i), §22.6(ii), §22.6(iii), §22.8(i), §22.8(ii), Profile Bille C. Carlson.

Encodings:

BibTeX

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Permutation symmetry for theta functions. J. Math. Anal. Appl. 378 (1), pp. 42–48.

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External Links:

ISSN 0022-247X, Document, FullText, MathReview (Mohammad Ahmad), ZentralBlatt

Referenced by:

§20.11(v), §20.7(i), §20.7(i), §20.7(ii), §20.7(ii), §20.7(ii), §20.7(iii), §20.7(iii), §20.7(vii), §20.7(vii), Profile Bille C. Carlson.

Encodings:

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18: 23.20 Mathematical Applications

… ►Then $\mathrm{\varnothing }\subseteq T\subseteq I\subseteq K\subseteq C$. …

19: Software Index

… ►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. …

20: 18.2 General Orthogonal Polynomials

… ►It is to be noted that, although formally correct, the results of (18.2.30) are of little utility for numerical work, as Hankel determinants are notoriously ill-conditioned. …