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References
- Daniel Shanks, Solved and unsolved problems in number theory. Vol. I, Spartan Books, Washington, D.C., 1962. MR 0160741 Ch. Fr. Gauss, Recherches Arithmétiques, reprinted by Blanchard, Paris, 1953.
- G. B. Mathews, Theory of numbers, Chelsea Publishing Co., New York, 1961. 2nd ed. MR 0126402
- Hans Reichardt (ed.), Gedenkband anlässlich des 100. Todestages am 23. Februar 1955, B. G. Teubner Verlagsgesellschaft, Leipzig, 1957 (German). MR 0088426 M. Kraitchik, Recherches sur la Théorie des Nombres, Gauthier-Villars, Paris, 1924, p. 55.
- Dov Jarden, Table of the ranks of apparition in Fibonacci’s sequence, Riveon Lematematika 1 (1946), 54 (Hebrew). MR 20565
- M. Lal, M. F. Jones, and W. J. Blundon, Numerical solutions of the Diophantine equation $y^{3}-x^{2}=k$, Math. Comp. 20 (1966), 322–325. MR 191871, DOI 10.1090/S0025-5718-1966-0191871-3
- Ove Hemer, Notes on the Diophantine equation $y^2-k=x^3$, Ark. Mat. 3 (1954), 67–77. MR 61115, DOI 10.1007/BF02589282
- Ove Hemer, On the solvability of the Diophantine equation $ax^2+by^2+cz^2=0$ in imaginary Euclidean quadratic fields, Ark. Mat. 2 (1952), 57–82. MR 49917, DOI 10.1007/BF02591382
- W. Ljunggren, On the diophantine equation $y^{2}-k=x^{3}$, Acta Arith. 8 (1962/63), 451–463. MR 158859, DOI 10.4064/aa-8-4-451-463 R. Robinson, "Table of integral solutions of $|{y^2} - {x^3}| < x$" UMT 125, MTAC, v. 5, 1951, p. 162. MTAC, v. 11, 1957, pp. 209–210, RMT 85. L. N. Karmazina & L. V. Kurochkina, Tablitsy interpoliatsionnykh koéfftsientov, Academy of Sciences of the USSR, Moscow, 1956. See MTAC, v. 12, 1958, p. 149, RMT 66. M. Sibuya, "Maximization with respect to partition of an interval and its application to the best systematic estimators of the exponential distribution," Ann. Math. Statist. (To appear.) A. A. Abramov, Tablitsy In $\Gamma (z)\upsilon$ kompleksnol oblasti, Izdat. Akad. Nauk SSSR, Moscow, 1953. (See MTAC, v. 12, 1958, pp. 150–151, RMT 70.) H. T. Davis, Tables of the Higher Mathematical Functions, Vols. 1, 2, Principia Press, Bloomington, Indiana, 1933 and 1935. Revised edition, entitled Tables of the Mathematical Functions, published by The Principia Press of Trinity University, San Antonio, Texas, 1963. (See Math. Comp., v. 19, 1965, pp. 696–698, RMT 131.) NBS Applied Mathematics Series, No. 17: Tables of Coulomb Wave Functions, U. S. Government Printing Office, Washington, D. C., 1952. (See MTAC, v. 7, 1953, pp. 101–102, RMT 1091.)
- Yudell L. Luke, Integrals of Bessel functions, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1962. MR 0141801
- Milton Abramowitz and Irene A. Stegun (eds.), Handbook of mathematical functions with formulas, graphs, and mathematical tables, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York; John Wiley & Sons, Inc., New York, 1984. Reprint of the 1972 edition; Selected Government Publications. MR 757537 E. N. Dekanosidze, Tablitsy tsilindrichskikh funktsiï ot dvukh peremennykh (Tables of cylinder functions), Acad. Sci. USSR, Moscow, 1956. (See MTAC, v. 12, 1958, pp. 239–240, RMT 107.) English translation published by Pergamon Press, New York, 1960. (See Math. Comp., v. 16, 1962, p. 383, RMT 36.)
- J. Boersma, On the computation of Lommel’s functions of two variables, Math. Comp. 16 (1962), 232–238. MR 146419, DOI 10.1090/S0025-5718-1962-0146419-2
- Kasaburô Harumi, Shigetoshi Katsura, and John W. Wrench Jr., Values of $(2/\pi )\int _{0}^{\infty }(\textrm {sin}\,t/t)^{n}dt$, Math. Comp. 14 (1960), 379. MR 122010, DOI 10.1090/S0025-5718-1960-0122010-7
- R. G. Medhurst and J. H. Roberts, Evaluation of the integral \[ I_n(b)={\textstyle 2\over \pi }\int ^\infty _0\left ({\sin x\over x}\right )^n \cos (bx)dx.\], Math. Comp. 19 (1965), 113–117. MR 172446, DOI 10.1090/S0025-5718-1965-0172446-8
- Rory Thompson, Evaluation of $I_{n}(b)=2\pi ^{-1}\int _{0}{}^\infty \,(\textrm {sin}x/x)^{n}\textrm {cos}(bx)\, dx$ and of similar integrals, Math. Comp. 20 (1966), 330–332. MR 192634, DOI 10.1090/S0025-5718-1966-0192634-5
- Henry E. Fettis and James C. Caslin, Ten place tables of the Jacobian elliptic functions. Part I, Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, Wright-Patterson Air Force Base, Ohio, 1965. Report No. ARL 65-180. MR 0201684 A. M. Legendre, Exercises de Calcul Intégral, v. 3, Paris, 1816. A. M. Legendre, Traité des Fonctions Elliptiques et des Intégrales Eulériennes, v. 2, Paris, 1826. A facsimile reproduction of Tables II and VIII therein appears in K. Pearson, Tables of the Complete and Incomplete Elliptic Integrals, reissued from Tome II of Legendre’s Traité des Fonctions Elliptiques, London, 1934. (See also Alan Fletcher, "Guide to tables of elliptic functions," MTAC, v. 3, 1948, pp. 229–281.)
- Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and physicists, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Band LXVII, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954. MR 0060642, DOI 10.1007/978-3-642-52803-3
- Carl Heuman, Tables of complete elliptic integrals, J. Math. Phys. Mass. Inst. Tech. 20 (1941), 127–206. MR 3572, DOI 10.1002/sapm1941201127
- Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and physicists, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Band LXVII, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954. MR 0060642, DOI 10.1007/978-3-642-52803-3 K. Hayashi, Tafeln der Besselschen, Theta-, Kugel-, und anderer Funktionen, Springer, Berlin, 1930.
- Otto Emersleben, Numerische Werte des Fehlerintegrals für $\sqrt {n\pi }$, Z. Angew. Math. Mech. 31 (1951), 393–394 (German). MR 45443, DOI 10.1002/zamm.19510311111 Editorial note: For reviews of earlier, related papers by the same author, see MTAC, v. 5, 1951, pp. 77–78, RMT 871; v. 11, 1957, pp. 109–110, RMT 56; ibid., p. 113–114, RMT 65. G. H. Stearman, "Is switching theory mathematics or engineering?," IEEE Trans. on Electronic Computers, v. EC-15, 1966, p. 124.
Additional Information
- © Copyright 1966 American Mathematical Society
- Journal: Math. Comp. 20 (1966), 616-638
- DOI: https://doi.org/10.1090/S0025-5718-66-99914-5