Bibliography E

♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

C. Eckart (1930)
The penetration of a potential barrier by electrons,

Phys. Rev. 35 (11), pp. 1303–1309.

External Links:

Document, ZentralBlatt.

Referenced by:

§15.18.

Encodings:

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U. Eckhardt (1980)
Algorithm 549: Weierstrass’ elliptic functions,

ACM Trans. Math. Software 6 (1), pp. 112–120.

Notes:

Single-precision Fortran, maximum accuracy 18D.

External Links:

ISSN 0098-3500, Document, TOMS module 549 (in GAMS).

Referenced by:

§23.24(iii).

Encodings:

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ECMNET Project (Web Site)

Notes:

Links to software for elliptic curve methods of factorization and primality testing.

External Links:

Home Page.

Referenced by:

§27.22.

Encodings:

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A. R. Edmonds (1974)
Angular Momentum in Quantum Mechanics,

3rd printing, with corrections, 2nd edition, Princeton University Press, Princeton, NJ.

Notes:

Reprinted in 1996.

External Links:

ISBN 0-691-02589-4, MathReview, ZentralBlatt.

Referenced by:

§14.30(i), §14.30(ii), §14.30(iii), §14.30(iv), §14.30(iv), §14.31(iii), §34.1, §34.13, §34.2, §34.3(i), §34.3(i), §34.3(ii), §34.3(iii), §34.3(iv), §34.3(vii), §34.3(vii), §34.5(i), §34.5(ii), §34.5(iii), §34.5(iv), §34.5(vi), §34.6, §34.7(i), §34.7(ii), §34.7(iv), §34.7(vi), Ch.34.

Encodings:

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H. M. Edwards (1974)
Riemann’s Zeta Function,

Academic Press,, New York-London.

Notes:

Pure and Applied Mathematics, Vol. 58. Reprinted by Dover Publications Inc., Mineola, NY, 2001.

External Links:

MathReview (Bruce C. Berndt), ZentralBlatt.

Referenced by:

Ch.25.

Encodings:

BibTeX
J. Edwards (1954)
A Treatise on the Integral Calculus,

Vol. 1-2, Chelsea Publishing Co., New York.

Notes:

Originally published by Macmillan, 1921-1930.

External Links:

ZentralBlatt.

Referenced by:

§19.11(i), §19.4(ii).

Encodings:

BibTeX
M. Edwards, D. A. Griggs, P. L. Holman, C. W. Clark, S. L. Rolston and W. D. Phillips (1999)
Properties of a Raman atom-laser output coupler,

J. Phys. B 32 (12), pp. 2935–2950.

External Links:

FullText.

Referenced by:

§12.17.

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G. P. Egorychev (1984)
Integral Representation and the Computation of Combinatorial Sums,

Translations of Mathematical Monographs, Vol. 59, American Mathematical Society, Providence, RI.

Notes:

Translated from the Russian by H. H. McFadden, Translation edited by Lev J. Leifman

External Links:

ISBN 0-8218-4512-8, MathReview, ZentralBlatt.

Referenced by:

§15.17(iv).

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U. T. Ehrenmark (1995)
The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature,

J. Comput. Appl. Math. 61 (1), pp. 43–72.

External Links:

ISSN 0377-0427, Document, MathReview (J. P. Singhal), ZentralBlatt.

Referenced by:

¶ ‣ §10.74(vii).

Encodings:

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M. Eichler and D. Zagier (1982)
On the zeros of the Weierstrass $\mathop{\wp\/}\nolimits$ -function,

Math. Ann. 258 (4), pp. 399–407.

External Links:

ISSN 0025-5831, Document, MathReview (Toyokazu Hiramatsu), ZentralBlatt.

Referenced by:

§23.13.

Encodings:

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Á. Elbert (2001)
Some recent results on the zeros of Bessel functions and orthogonal polynomials,

J. Comput. Appl. Math. 133 (1-2), pp. 65–83.

External Links:

ISSN 0377-0427, Document, MathReview (N. Hayek Calil), ZentralBlatt.

Referenced by:

§10.21(iv).

Encodings:

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Á. Elbert and A. Laforgia (1994)
Interlacing properties of the zeros of Bessel functions,

Atti Sem. Mat. Fis. Univ. Modena XLII (2), pp. 525–529.

External Links:

ISSN 0041-8986, MathReview (Evangelos Ifantis), ZentralBlatt.

Referenced by:

§10.21(i).

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Á. Elbert and A. Laforgia (1997)
An upper bound for the zeros of the derivative of Bessel functions,

Rend. Circ. Mat. Palermo (2) 46 (1), pp. 123–130.

External Links:

ISSN 0009-725X, MathReview (Boro Döring), ZentralBlatt.

Referenced by:

§10.21(vii).

Encodings:

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Á. Elbert and A. Laforgia (2000)
Further results on McMahon’s asymptotic approximations,

J. Phys. A 33 (36), pp. 6333–6341.

External Links:

ISSN 0305-4470, Document, MathReview (R. G. Aĭrapetyan), ZentralBlatt.

Referenced by:

§10.21(vi).

Encodings:

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Á. Elbert and A. Laforgia (2008)
The zeros of the complementary error function,

Numer. Algorithms 49 (1-4), pp. 153–157.

External Links:

ISSN 1017-1398, Document, FullText, MathReview (Boro Döring), ZentralBlatt.

Referenced by:

§7.13(ii).

Encodings:

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E. Elizalde (1986)
An asymptotic expansion for the first derivative of the generalized Riemann zeta function,

Math. Comp. 47 (175), pp. 347–350.

External Links:

ISSN 0025-5718, FullText, MathReview (S. Audinarayana Moorthy), ZentralBlatt.

Referenced by:

§25.11(xii), §25.11(xii).

Encodings:

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E. Elizalde (1995)
Ten Physical Applications of Spectral Zeta Functions,

Lecture Notes in Physics. New Series m: Monographs, Vol. 35, Springer-Verlag, Berlin.

External Links:

ISBN 3-540-60230-5, MathReview (Alfred Actor), ZentralBlatt.

Referenced by:

§25.17.

Encodings:

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D. Elliott (1971)
Uniform asymptotic expansions of the Jacobi polynomials and an associated function,

Math. Comp. 25 (114), pp. 309–315.

External Links:

FullText, MathReview, ZentralBlatt.

Referenced by:

§18.15(i).

Encodings:

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D. Elliott (1998)
The Euler-Maclaurin formula revisited,

J. Austral. Math. Soc. Ser. B 40 (E), pp. E27–E76 (electronic).

External Links:

ISSN 0334-2700, FullText, MathReview (J. Németh), ZentralBlatt.

Referenced by:

¶ ‣ §2.10(i).

Encodings:

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E. B. Elliott (1903)
A formula including Legendre’s $EK^{{\prime}}+KE^{{\prime}}-KK^{{\prime}}=\frac{1}{2}\pi$ ,

Messenger of Math. 33, pp. 31–32.

Notes:

Errata on p. 45 of the same volume.

External Links:

ZentralBlatt.

Referenced by:

§15.16.

Encodings:

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W. J. Ellison (1971)
Waring’s problem,

Amer. Math. Monthly 78 (1), pp. 10–36.

External Links:

FullText, MathReview (J. W. S. Cassels), ZentralBlatt.

Referenced by:

§27.13(iii), §27.13(iii).

Encodings:

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S. P. EraŠevskaja, E. A. Ivanov, A. A. Pal’cev and N. D. Sokolova (1973)
Tablicy sferoidal’nyh volnovyh funkcii i ih pervyh proizvodnyh. Tom I,

Izdat. “Nauka i Tehnika”, Minsk (Russian).

Notes:

Translated title: Tables of Spheroidal Wave Functions and Their First Derivatives.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§30.17.

Encodings:

BibTeX
S. P. EraŠevskaja, E. A. Ivanov, A. A. Pal’cev and N. D. Sokolova (1976)
Tablicy sferoidal’nyh volnovyh funkcii iih pervyh proizvodnyh. Tom II,

Izdat. “Nauka i Tehnika”, Minsk (Russian).

Notes:

Edited by V. I. Krylov. Translated title: Tables of Spheroidal Wave Functions and Their First Derivatives.

External Links:

MathReview.

Referenced by:

§30.17.

Encodings:

BibTeX
N. Ercolani and A. Sinha (1989)
Monopoles and Baker functions,

Comm. Math. Phys. 125 (3), pp. 385–416.

External Links:

ISSN 0010-3616, Link, MathReview (Jacques Hurtubise), ZentralBlatt.

Referenced by:

§21.9.

Encodings:

BibTeX

A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi (1954a)
Tables of Integral Transforms. Vol. I,

McGraw-Hill Book Company, Inc., New York-Toronto-London.

Notes:

Table errata: Math. Comp. v. 66 (1997), no. 220, p. 1766–1767, v. 65 (1996), no. 215, p. 1384, v. 50 (1988), no. 182, p. 653, v. 41 (1983), no. 164, p. 778–779, v. 27 (1973), no. 122, p. 451, v. 26 (1972), no. 118, p. 599, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239-240.

External Links:

MathReview (H. Kober), ZentralBlatt.

Referenced by:

§1.14(viii), §10.22(vi), §10.32(iv), §10.43(vi), §10.9(iv), §11.10(x), §11.5(iii), §11.7(v), §11.9(iv), ¶ ‣ §12.12, §12.5(iv), ¶ ‣ §13.10(ii), §13.10(iii), §13.10(iv), §13.23(i), §13.23(ii), §14.17(v), §15.14, §16.20, §16.5, §18.17(ix), §20.10(ii), §20.10(iii), §25.5(ii), ¶ ‣ §5.13, §6.14(iii), §6.7(iv), §7.14(iii), §7.7(iii), §8.14.

Encodings:

BibTeX
A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi (1954b)
Tables of Integral Transforms. Vol. II,

McGraw-Hill Book Company, Inc., New York-Toronto-London.

Notes:

Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1385, v. 41 (1983), no. 164, pp. 779–780, v. 31 (1977), no. 138, p. 614, v. 31 (1977), no. 137, pp. 328–329, v. 26 (1972), no. 118, p. 599, v. 25 (1971), no. 113, p. 199, v. 23 (1969), no. 106, p. 468.

External Links:

MathReview (H. Kober), ZentralBlatt.

Referenced by:

§1.14(viii), §10.22(v), §10.22(vi), §10.43(v), §10.43(vi), ¶ ‣ §12.12, §13.10(v), §13.10(v), §13.10(vi), §13.23(iii), §13.23(v), §15.14, §15.14, §18.17(ix), ¶ ‣ §5.13, §8.14.

Encodings:

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A. Erdélyi (1941a)
Generating functions of certain continuous orthogonal systems,

Proc. Roy. Soc. Edinburgh. Sect. A. 61, pp. 61–70.

External Links:

MathReview (G. Szegö), ZentralBlatt.

Referenced by:

§12.16.

Encodings:

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A. Erdélyi (1941b)
On Lamé functions,

Philos. Mag. (7) 31, pp. 123–130.

External Links:

MathReview (G. Szegö), ZentralBlatt.

Referenced by:

§29.3(ii).

Encodings:

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A. Erdélyi (1941c)
On algebraic Lamé functions,

Philos. Mag. (7) 32, pp. 348–350.

External Links:

MathReview (G. Szegö), ZentralBlatt.

Referenced by:

§29.17(ii).

Encodings:

BibTeX
A. Erdélyi (1942a)
Integral equations for Heun functions,

Quart. J. Math., Oxford Ser. 13, pp. 107–112.

External Links:

Document, MathReview (E. Rothe), ZentralBlatt.

Referenced by:

§31.10(i).

Encodings:

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A. Erdélyi (1942b)
The Fuchsian equation of second order with four singularities,

Duke Math. J. 9 (1), pp. 48–58.

External Links:

Document, MathReview (R. E. Langer), ZentralBlatt.

Referenced by:

§31.11(i).

Encodings:

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A. Erdélyi (1944)
Certain expansions of solutions of the Heun equation,

Quart. J. Math., Oxford Ser. 15, pp. 62–69.

External Links:

Document, MathReview (R. E. Langer), ZentralBlatt.

Referenced by:

§31.11(i), §31.11(i), §31.9(i).

Encodings:

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A. Erdélyi (1956)
Asymptotic Expansions,

Dover Publications Inc., New York.

External Links:

MathReview (N. D. Kazarinoff), ZentralBlatt.

Referenced by:

Ch.2.

Encodings:

BibTeX
A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi (1953a)
Higher Transcendental Functions. Vol. I,

McGraw-Hill Book Company, Inc., New York-Toronto-London.

Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1385, v. 41 (1983), no. 164, p. 778, v. 30 (1976), no. 135, p. 675, v. 25 (1971), no. 115, p. 635, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 112, p. 999, v. 24 (1970), no. 110, p. 504, v. 17 (1963), no. 84, p. 485.

External Links:

MathReview (E. T. Copson), ZentralBlatt.

Referenced by:

§13.1, §13.10(ii), §13.10(iv), §13.12, §13.13(i), §13.16(ii), §13.16(iii), §13.23(i), §13.23(ii), §13.25, §13.4(i), §13.4(ii), §13.9(i), §13.9(ii), Ch.13, §14.1, §14.10, ¶ ‣ §14.12(ii), §14.12(i), §14.12(ii), §14.13, §14.13, §14.17(ii), §14.17(iv), §14.18(ii), §14.18(iii), §14.18(iv), §14.19(i), §14.19(ii), §14.19(iii), §14.19(iv), §14.20(v), §14.21(iii), §14.25, §14.28(i), §14.28(ii), §14.3(iii), §14.3(iii), §14.3(iv), §14.5(iii), §14.5(iv), §14.6(i), §14.6(ii), §14.7(iv), §14.8(i), §14.8(ii), Ch.14, ¶ ‣ §15.16, §15.4(iii), §15.5(i), §15.6, ¶ ‣ §15.8(v), §15.8(ii), §15.8(v), §15.9(iii), Ch.15, §16.12, §16.12, §16.13, §16.14(i), §16.14(ii), §16.15, §16.16(i), §16.16(ii), §16.18, §16.20, §16.20, §16.21, ¶ ‣ §16.4(ii), §16.5, ¶ ‣ §16.6, Ch.16, §19.21(i), §19.28, §19.5, §24.16(iii), §24.5(i), §24.7(i), §24.7(ii), §24.8(i), Ch.24, §25.11(v), §25.11(vi), §25.12(ii), §25.14(i), §25.14(ii), §25.5(i), §25.5(iii), §25.8, Ch.25, §5.7(i), Ch.5.

Encodings:

BibTeX
A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi (1953b)
Higher Transcendental Functions. Vol. II,

McGraw-Hill Book Company, Inc., New York-Toronto-London.

Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778, v. 36 (1981), no. 153, p. 315, v. 30 (1976), no. 135, p. 675, v. 29 (1975), no. 130, p. 670, v. 26 (1972), no. 118, p. 598, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239, v. 17 (1963), no. 84, p. 485.

External Links:

MathReview (E. T. Copson), ZentralBlatt.

Referenced by:

§10.22(iv), §10.22(vi), ¶ ‣ §10.23(iii), ¶ ‣ §10.23(iii), §10.23(iv), §10.32(i), §10.32(iii), §10.32(iv), §10.43(iv), §10.43(vi), §10.44(iv), §10.60(iv), §10.9(i), §10.9(iii), §10.9(iv), §11.10(vi), §11.4(i), Ch.11, ¶ ‣ §12.12, §12.12, §12.13(i), §12.5(iv), Ch.12, §18.16(vi), §18.17(i), §18.17(viii), ¶ ‣ §18.30, §19.1, §19.10(i), §19.14(ii), §19.25(vi), §19.5, ¶ ‣ §19.7(ii), §19.9(i), Ch.19, §20.9(i), §22.15(ii), ¶ ‣ §23.6(iv), Ch.23, §8.13(i), §8.14, §8.3(i), §8.4, §8.6(iii), §8.7, Ch.8.

Encodings:

BibTeX
A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi (1955)
Higher Transcendental Functions. Vol. III,

McGraw-Hill Book Company, Inc., New York-Toronto-London.

Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778.

External Links:

MathReview (E. T. Copson), ZentralBlatt.

Referenced by:

§10.46, §27.2(i), Ch.27, Table 28.1.1, §28.10(iii), §28.2(iii), §28.2(v), §29.1, §29.10, §29.11, §29.14, §29.17(i), §29.17(iii), §29.18(i), §29.18(ii), §29.18(iii), §29.18(iii), §29.2(i), §29.2(ii), §29.3(i), §29.3(ii), §29.3(ii), §29.3(iv), §29.5, §29.6(i), §29.6(ii), §29.6(iii), §29.6(iv), §29.8, §29.8, Ch.29, §30.1, §30.10, §30.11(v), §30.11(vi), §30.13(i), §30.14(i), §30.9(iii), Ch.30, §31.2(i), §31.4, §31.5, Ch.31.

Encodings:

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R. Ernvall (1979)
Generalized Bernoulli numbers, generalized irregular primes, and class number,

Ann. Univ. Turku. Ser. A I 178, pp. 1–72.

External Links:

ISSN 0082-7002, MathReview (Wells Johnson), ZentralBlatt.

Referenced by:

§24.10(ii).

Encodings:

BibTeX
F. H. L. Essler, H. Frahm, A. R. Its and V. E. Korepin (1996)
Painlevé transcendent describes quantum correlation function of the $XXZ$ antiferromagnet away from the free-fermion point,

J. Phys. A 29 (17), pp. 5619–5626.

External Links:

ISSN 0305-4470, Document, MathReview (Estelle L. Basor), ZentralBlatt.

Referenced by:

¶ ‣ §32.16.

Encodings:

BibTeX
T. Estermann (1959)
On the representations of a number as a sum of three squares,

Proc. London Math. Soc. (3) 9, pp. 575–594.

External Links:

Document, MathReview (S. Chowla), ZentralBlatt.

Referenced by:

§20.12(i).

Encodings:

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Euclid (1908)
The Thirteen Books of Euclid’s Elements,

Cambridge University Press, Cambridge.

Notes:

Translated from the text of Heiberg, with introduction and commentary by Thomas L. Heath. Reprint of the Cambridge Univeristy second edition by Dover Publications, Inc., New York, 1956.

External Links:

MathReview, ZentralBlatt.

Referenced by:

§27.2(i).

Encodings:

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L. Euler (1768)
Institutiones Calculi Integralis,

Opera Omnia (1), Vol. 11, pp. 110–113.

Referenced by:

§25.12(i).

Encodings:

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G. A. Evans and J. R. Webster (1999)
A comparison of some methods for the evaluation of highly oscillatory integrals,

J. Comput. Appl. Math. 112 (1-2), pp. 55–69.

External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt.

Referenced by:

§3.5(vii).

Encodings:

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W. D. Evans, W. N. Everitt, K. H. Kwon and L. L. Littlejohn (1993)
Real orthogonalizing weights for Bessel polynomials,

J. Comput. Appl. Math. 49 (1-3), pp. 51–57.

External Links:

ISSN 0377-0427, Document, MathReview (B. D. Agrawal), ZentralBlatt.

Referenced by:

§18.34(ii).

Encodings:

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W. N. Everitt and D. S. Jones (1977)
On an integral inequality,

Proc. Roy. Soc. London Ser. A 357, pp. 271–288.

External Links:

ISSN 0962-8444, FullText, MathReview, ZentralBlatt.

Referenced by:

§10.37.

Encodings:

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J. A. Ewell (1990)
A new series representation for $\mathop{\zeta\/}\nolimits(3)$ ,

Amer. Math. Monthly 97 (3), pp. 219–220.

External Links:

ISSN 0002-9890, FullText, MathReview (Christian Radoux), ZentralBlatt.

Referenced by:

§25.8.

Encodings:

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H. Exton (1983)
The asymptotic behaviour of the inhomogeneous Airy function $\mathop{\mathrm{Hi}\/}\nolimits(z)$ ,

Math. Chronicle 12, pp. 99–104.

External Links:

ISSN 0581-1155, MathReview (Ram Kishore Saxena), ZentralBlatt.

Referenced by:

§9.12(vii).

Encodings:

BibTeX
J. Écalle (1981a)
Les fonctions résurgentes. Tome I,

Université de Paris-Sud Département de Mathématique, Orsay (French).

External Links:

MathReview (Carlos A. Berenstein).

Referenced by:

§2.7(ii).

Encodings:

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J. Écalle (1981b)
Les fonctions résurgentes. Tome II,

Université de Paris-Sud Département de Mathématique, Orsay (French).

External Links:

MathReview (Carlos A. Berenstein).

Referenced by:

§2.7(ii).

Encodings:

BibTeX