tables of zeros
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31—40 of 62 matching pages
31: Bibliography G
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A table of integrals of the exponential integral.
J. Res. Nat. Bur. Standards Sect. B 73B, pp. 191–210.
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Number-Divisor Tables.
British Association Mathematical Tables, Vol. VIII, Cambridge University Press, Cambridge, England.
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Tables of Partitions.
Royal Society Math. Tables, Vol. 4, Cambridge University Press.
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A table of partitions.
Proc. London Math. Soc. (2) 39, pp. 142–149.
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A table of partitions (II).
Proc. London Math. Soc. (2) 42, pp. 546–549.
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32: 13.30 Tables
§13.30 Tables
… ►Slater (1960) tabulates for , , and , 7–9S; for and , 7D; the smallest positive -zero of for and , 7D.
Abramowitz and Stegun (1964, Chapter 13) tabulates for , , and , 8S. Also the smallest positive -zero of for and , 7D.
33: 29.12 Definitions
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►In consequence they are doubly-periodic meromorphic functions of .
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►The prefixes , , , , , , , indicate the type of the polynomial form of the Lamé polynomial; compare the 3rd and 4th columns in Table 29.12.1.
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►With the substitution every Lamé polynomial in Table 29.12.1 can be written in the form
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§29.12(iii) Zeros
►Let denote the zeros of the polynomial in (29.12.9) arranged according to …34: 14.33 Tables
§14.33 Tables
… ►Zhang and Jin (1996, Chapter 4) tabulates for , , 7D; for , , 8D; for , , 8S; for , , 8D; for , , , , 8S; for , , 8S; for , , , 5D; for , , 7S; for , , 8S. Corresponding values of the derivative of each function are also included, as are 6D values of the first 5 -zeros of and of its derivative for , .
Žurina and Karmazina (1963) tabulates the conical functions for , , 7S; for , , 7S. Auxiliary tables are included to assist computation for larger values of when .
35: Bibliography P
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Tablitsy nepolnoi gamma-funktsii.
Vyčisl. Centr Akad. Nauk SSSR, Moscow (Russian).
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Tables of Digamma and Trigamma Functions.
In Tracts for Computers, No. 1, K. Pearson (Ed.),
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Tables of the Incomplete Elliptic Integrals of the First and Third Kind.
Technical report
Curtiss-Wright Corp., Research Division, Quehanna, PA.
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Tables of the Incomplete -function.
Biometrika Office, Cambridge University Press, Cambridge.
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Tables of the Incomplete Beta-function.
2nd edition, Published for the Biometrika Trustees at the Cambridge
University Press, Cambridge.
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36: Bibliography D
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Complex zeros of linear combinations of spherical Bessel functions and their derivatives.
SIAM J. Math. Anal. 4 (1), pp. 128–133.
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Tables of Higher Mathematical Functions I.
Principia Press, Bloomington, Indiana.
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Sur les zéros réels des polynômes de Bernoulli.
Ann. Inst. Fourier (Grenoble) 41 (2), pp. 267–309 (French).
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On multiple zeros of Bernoulli polynomials.
Acta Arith. 134 (2), pp. 149–155.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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37: Bibliography S
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A global Newton method for the zeros of cylinder functions.
Numer. Algorithms 18 (3-4), pp. 259–276.
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Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros.
Math. Comp. 70 (235), pp. 1205–1220.
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Some properties of polynomial sets of type zero.
Duke Math. J. 5, pp. 590–622.
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Tables of the integro-exponential functions.
Acta Astronom. 18, pp. 289–311.
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The real zeros of Struve’s function.
SIAM J. Math. Anal. 1 (3), pp. 365–375.
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38: Bibliography M
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Chebyshev Polynomials.
Chapman & Hall/CRC, Boca Raton, FL.
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Inequalities for the zeros of Bessel functions.
SIAM J. Math. Anal. 8 (1), pp. 166–170.
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Tables of Generalized Exponential Integrals.
NPL Mathematical Tables, Vol. III, Her Majesty’s Stationery Office, London.
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Table of the ratio: Area to bounding ordinate, for any portion of normal curve.
Biometrika 18, pp. 395–400.
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Jacobian Elliptic Function Tables.
Dover Publications Inc., New York.
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39: 5.2 Definitions
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5.2.1
.
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►It is a meromorphic function with no zeros, and with simple poles of residue at .
is entire, with simple zeros at .
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5.2.3
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40: 23.20 Mathematical Applications
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►The curve is made into an abelian group (Macdonald (1968, Chapter 5)) by defining the zero element as the point at infinity, the negative of by , and generally on the curve iff the points , , are collinear.
It follows from the addition formula (23.10.1) that the points , , have zero sum iff , so that addition of points on the curve corresponds to addition of parameters on the torus ; see McKean and Moll (1999, §§2.11, 2.14).
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►If any of these quantities is zero, then the point has finite order.
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►For extensive tables of elliptic curves see Cremona (1997, pp. 84–340).
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