Saalschützian series

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1: 17.4 Basic Hypergeometric Functions

… ►The series (17.4.1) is said to be balanced or Saalschützian when it terminates, $r=s$, $z=q$, and …

2: Bibliography K

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An extension of Saalschütz’s summation theorem for the series ${}_{r+3}{}^{}F_{r+2}^{}$ . Integral Transforms Spec. Funct. 24 (11), pp. 916–921.

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External Links:

ISSN 1065-2469, Document, FullText, MathReview (Christian Lavault), ZentralBlatt

Referenced by:

§16.4(ii), §16.4(ii).

Encodings:

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3: 24.1 Special Notation

… ►It was used in Saalschütz (1893), Nielsen (1923), Schwatt (1962), and Whittaker and Watson (1927). … ►The secant series (4.19.5) first occurs in the work of Gregory in 1671. …

4: 16.4 Argument Unity

… ►When $k=1$ the function is said to be balanced or Saalschützian. … ►

Pfaff–Saalschütz Balanced Sum

… ►when the series on the right terminates and the series on the left converges. … ►

§16.4(v) Bilateral Series

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5: Bibliography S

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Vorlesungen über die Bernoullischen Zahlen, ihren Zusammenhang mit den Secanten-Coefficienten und ihre wichtigeren Anwendungen. Springer-Verlag, Berlin (German).

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External Links:

ZentralBlatt

Referenced by:

§24.1.

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On Lindelöf’s error bound for Stirling’s series. J. Reine Angew. Math. 404, pp. 135–139.

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External Links:

ISSN 0075-4102, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§5.11(ii).

Encodings:

BibTeX

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An Introduction to the Operations with Series. 2nd edition, Chelsea Publishing Co., New York.

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Notes:

This is a reprint, with corrections, of the first edition [University of Pennsylvania Press, Philadelphia, Pa., 1924].

External Links:

MathReview, ZentralBlatt

Referenced by:

§24.1, §24.6.

Encodings:

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Asymptotic series of generalized Lambert $W$ function. ACM Commun. Comput. Algebra 47 (3), pp. 75–83.

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External Links:

FullText, ZentralBlatt

Referenced by:

§4.13, §4.13.

Encodings:

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An Introduction to Basic Fourier Series. Developments in Mathematics, Vol. 9, Kluwer Academic Publishers, Dordrecht.

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External Links:

ISBN 1-4020-1221-7, MathReview (P. D. F. Ion), ZentralBlatt

Referenced by:

§17.3(i).

Encodings:

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