Bernoulli Bibliography

H


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HA CHUNG-WEI: see CHANG KU-YOUNG, KWON SOUN-HI

HACHIMORI Y., ICHIMURA H.,
[1] Semi-local units modulo Gauss sums, Manuscripta Math. 95 (1998), no. 3, 377-395.
Z980.22003; M99h:11120

HADAMARD J.,
[1] Sur la série de Stirling, Proc. Fifth Intern. Congress Math., 1 (1913), 303-305.
J44.0515.02

HAIGH C.W.,
[1] Newton's identities, generalised cycle-indices, universal Bernoulli numbers and truncated Schur-functions, J. Math. Chem. (to appear).

HALBRITTER U.,
[1] Eine elementare Methode zur Berechnung von Zetafunktionen reell-quadratischer Zahlkörper, Math. Ann., 271 (1985), no. 3, 359-379.
Z541.12008; M86i:11067; R1986,2A460

[2] Berechnung der Werte von verallgemeinerten Zetafunktionen reell-quadratischer Zahlkörper mittels Dedekindscher Summen, J. Number Theory, 17 (1983), no. 3, 285-322.
Z522.12013; M85h:11072; R1984,5A115

[3] Anwendung einer Summationsformel auf Dirichletsche Reihen und verallgemeinerte Dedekindsche Summen, Acta Arith., 43 (1984), no. 4, 349-359.
Z492.10008; M86b:11032; R1985,1A167

[4] Some new reciprocity formulas for generalized Dedekind sums, Resultate Math. 8 (1985), no. 1, 21-46.
Z577.10011; M87a:11043

HALL R.R., WILSON J.C.,
[1] On reciprocity formulae for inhomogeneous and homogeneous Dedekind sums. Math. Proc. Cambridge Philos. Soc., 114 (1993), no. 1, 9-24.
Z783.11021; M94c:11037

HALL R.R., WILSON J.C., ZAGIER D.,
[1] Reciprocity formulae for general Dedekind-Rademacher sums, Acta Arith., 73 (1995), no. 4, 389-396.
Z847.11020; M96j:11054; R1996,11A182

HALL T.G.,
[1] Art calcul of finite differences, Encycl. Pure Math., (1847), 261-270.

HAMILTON W.R.,
[1] On an expression for the numbers of Bernoulli, by means of a definite integral, and on some connected progresses of summation and integration, Phil. Mag., 23 (1843), 360-367.

HAMMOND J.,
[1] On the relation between Bernoulli's numbers and the binomial coefficients, Proc. London Math. Soc., 7 (1875), 9-14.
J08.0144.02

HAN GUO-NIU,
[1] Calcul Denertien, Publ. Inst. Rech. Math. Avan., 1991, no. 476, 1-119.
M93h:05169; R1993,4A121

[2] Symétries trivariés sur les nombres de Genocchi. European J. Combin. 17 (1996), no. 4, 397--407.
Z852.0500; M97e:05015

HAN GUO-NIU, ZENG JIANG,
[1] On a $q$-sequence that generalizes the median Genocchi numbers. Ann. Sci. Math. Québec, 23 (1999), no. 1, 63-72.
Zpre01678924; M2000g:11014; R1999,3A230

HAN G.-N.; RANDRIANARIVONY A.; ZENG J.,
[1] Un autre $q$-analogue des nombres d'Euler. Sém. Lothar. Combin. 42 (1999), Art. B42e, 22 pp. (electronic).
M2000g:11013

HANSEN E.R.,
[1] A Table of Series and Products, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1975.

HAO F.H., PARRY C.J.,
[1] Generalized Bernoulli numbers and m-regular primes, Math. Comp., 43 (1984), no. 167, 273-288.
Z548.12006; M85h:11062; R1985,6A111

HARDER G.,
[1] Über spezielle Werte von L-Funktionen, Mitt. Math. Ges. Hamburg, 11 (1982), no. 1, 121-127.
Z503.12009; M84b:12019

HARDER G., PINK R.,
[1] Modular konstruierte unverzweigte abelsche $p$-Erweiterungen von $ Q(\zeta_p)$ und die Struktur ihrer Galoisgruppen. Math. Nachr., 159 (1992), 83-99.
Z773.11069; M95b:11100

HARDY G.H.,
[1] A formula of Ramanujan, J. London Math. Soc., 3 (1928), 238-240.

[2] Divergent Series. Oxford University Press, 1949. xvi + 396 pp.
Z32.05801; M11-25a

HARDY G.H., WRIGHT E.M.,
[1] An introduction to the theory of numbers, 5th Ed., Oxford Science Publications, 1979.
Z423.10001; M81i:10002; R1961,5A162K

HARE D.E.G.,
[1] Computing the principal branch of log-Gamma, J. Algorithms 25 (1997), no. 2, 221-236.
Z887.68055

HÄRKÖNEN K.,
[1] On the Diophantine equation $x^l+y^l=cz^l$ in the third case, Ann. Univ. Turku., Ser. A1, (1980), no. 180, 1-16.
M81m:10023; R1981,5A134

HARTREE D.R.,
[1] Numerical Analysis, Clarendon Press, Oxford, 1952. xiv +287 pp.
Z49.35905; M14-690f; R1953,458PEII

HARTUNG P.: see CHOWLA S., HARTUNG P.

HARUKI H., RASSIAS T.M.,
[1] New integral representations for Bernoulli and Euler polynomials, J. Math. Anal. Appl., 175 (1993), no. 1, 81-90.
Z776.11009; M94e:39016

HASHIMOTO K., KOSEKI H.,
[1] Class numbers of definite unimodular Hermitian forms over the rings of imaginary quadratic fields, Tôhoku Math. J. (2), 41 (1989), no. 1, 1-30.
Z668.10029; M90g:11050; R1990,5A123

HASSE H.,
[1] Ein Summierungsverfahren für die Riemannsche $\zeta$-Reihe, Math. Z., 32 (1930), 458-464.
J56.0894.03

[2] Über die gewöhnlichen und verallgemeinerten Bernoullischen Zahlen, Simposio di Analisi, v. II, (1961), 67-72, "Archimedes Commemoration in 20th Century", Siracusa.
Z123.03903; M30#4712

[3] Sulla generalizzazione di Leopoldt dei numeri di Bernoulli e sua applicazione alla divisibilità del numero della classi nei corpi numerici abeliani, Rend. Math. e Applic., 21 (1962), 9-27.
Z111.04501; M25#3925; R1963,3A168

[4] Über die Bernoullischen Zahlen, Leopoldina, Reihe 3, 1962/63, 8/9 (1965), 159-167.
Z166.05003; R1966,4A95

[5] Vandiver's congruence for the relative class-number of the p-th cyclotomic field, J. Math. Anal. Appl., 15 (1966), 87-90.
Z139.28103; M33#4040; R1967,8A101

[6] Number Theory, Akademie-Verlag, Berlin, 1979. (A corrected and enlarged translation of Hasse, Zahlentheorie, 3rd Edition, Akademie-Verlag, Berlin, 1969.)
Z423.12001; M40#7185; R1970,2A305K

HATADA K.,
[1] On the values at rational integers of the p-adic Dirichlet L-functions, J. Math. Soc. Japan, 31 (1979), no. 1, 7-27.
Z399.12003; M80f:12010; R1979,9A334

[2] Mod 1 distribution of Fermat and Fibonacci quotients and values of zeta functions at $2-p$, Comment. Math. Univ. St. Paul., 36 (1987), no. 1, 41-51.
Z641.12008; M88i:11085; R1988,8A111

[3] Notes on Bernoulli numbers, Sci. Rep. Fac. Ed. Gifu Univ. Natur. Sci., 19 (1995), no. 2, 157-166.
Z825.11010; M96c:11024

[4] On the limits of $p$-adic sequences of averages. Sci. Rep. Fac. Ed. Gifu Univ. Natur. Sci. 24 (2000), no. 2, 7-13.

HAUSS M.,
[1] Verallgemeinerte Stirling, Bernoulli und Euler Zahlen, deren Anwendungen und schnell konvergente Reihen f\"ur Zeta Funktionen. (German) [Generalized Stirling, Bernoulli and Euler numbers and their applications and fast convergent series for zeta functions] Dissertation, RWTH Aachen, Aachen, 1995. Berichte aus der Mathematik. [Reports from Mathematics] Verlag Shaker, Aachen, 1995. iv+209 pp.
Z867.11010; M97c:11029

[2] An Euler-Maclaurin-type formula involving conjugate Bernoulli polynomials and an application to $\zeta(2m+1)$. Commun. Appl. Anal. 1 (1997), no. 1, 15-32.
Z877.11009; M98b:11019

[3] A Boole-type formula involving conjugate Euler polynomials. Charlemagne and his heritage. 1200 years of civilization and science in Europe, Vol. 2 (Aachen, 1995), 361-375, Brepols, Turnhout, 1998.
M99k:11030

HAUSS M.: see BUTZER P.L., FLOCKE S., HAUSS M.

HAUSS M.: see BUTZER P.L. et al

HAUSSNER R.,
[1] Zur Theorie der Bernoull'ischen und Euler'schen Zahlen, Nachr. Kgl. Gesellsch. Wiss., Göttingen, 21 (1893), 777-809.
J25.0414.01

[2] Independente Darstellung der Bernoull'ischen und Euler'schen Zahlen durch Determinanten, Zeitsch. f. Math. und Phys., 39 (1894), 183-188.
J25.0413.02

[3] Über verallgemeinerte Eulersche Zahlen und Tangentenkoeffizienten, Ber. über die Verhandl. der Königl. Sächs. Ges. der Wiss. Leipzig, Math.-phys. Kl., 62 (1910), 386-418.
J41.0499.01

[4] Über verallgemeinte Tangenten- und Sekantenkoeffizienten, Arch. der Math. u. Phys. (3), 17 (1911), 333-337.
J42.0208.02

HEASLET M.A.: see USPENSKY J.V., HEASLET M.A.

HEATH R.,
[1] Euler sums, Tech. Engng. News, 57 (1956), no. 5, 58-60.
R1957,2444

HEATH-BROWN D.R.: see ADLEMAN L.M., HEATH-BROWN D.R.

Hegazi, A. S.; Mansour, M.,
[1] A note on $q$-Bernoulli numbers and polynomials. J. Nonlinear Math. Phys. 13 (2006), no. 1, 9--18.
M2007b:33039

HENNEBERGER, M.,
[1] Beiträge zur Theorie der Integrale der Bernoullischen Funktionen, Dissertation, Universität Bern, 1901, 66p.
J34.0492.04

HENSEL K.,
[1] Gedächtnisrede auf E.E. Kummer, Abhandl. zur Geschichte der Math. Wiss., Heft 29 (1910), 18-31.
J41.0015.03

[2] E.E. Kummer und der grosse Fermatsche Satz, Reden Marburger Akad. No. 23, N.G. Elwertsche Verlagsbuchhandlung, 1910.
J41.0016.01

HERBRAND J.,
[1] Sur les classes des corps circulaires, J. Math. Pures Appl. (9), 11 (1932), 417-441.
J58.0180.02; Z6.00802

HERGET W.,
[1] Bernoulli-Polynome in $Z_n$, Dissertation, TU Braunschweig, 1975.
Z359.10016

[2] Minimum periods modulo $n$ for Bernoulli numbers, Fibonacci Quart., 16 (1978), no. 6, 544-548.
Z397.10007; M80f:10011

[3] Bernoulli-Polynome in den Restklassenringen $Z\sb{n}$, Glas. Mat., Ser. 3, 14 (34)(1979), no. 1, 27-33.
Z402.10008; M80j:10018; R1979,12A88

[4] Minimum periods modulo $n$ for Bernoulli polynomials, Fibonacci Quart., 20 (1982), 106-110.
Z482.10011; M84b:10018

HERGLOTZ G.,
[1] Über das quadratische Reziprozitätsgesetz in imaginären quadratischen Zahlkörpern, Ber. Verh. Sächs. Akad. Wiss. Leipzig, 73 (1921), 303-310.
J48.0170.02

[2] Über die Entwicklungskoeffizienten der Weierstrasschen $\wp$-Funktionen, Ber. Verh. Sächs. Akad. Wiss. Leipzig, 74 (1922), 269-289.
J48.0438.03

HERMES H.: see EBBINGHAUS H.-D. et al.

HERMITE CH.,
[1] Extrait d'une lettre de M. Hermite à M. Borchardt (sur les nombres de Bernoulli), J. Reine Angew. Math., 81 (1876), 93-95.
J07.0131.01

[2] Sur la formule de Maclaurin, J. Reine Angew. Math., 84 (1877), 64-69.
J09.0182.02

[3] Extrait d'une lettre, Nouv. Corres. Math., 6 (1880), 121-122.

[4] Lettre de M. Ch. Hermite à M. Borchardt sur la fonction de Jacob Bernoulli, J. Reine Angew. Math., 79 (1875), 339-344.
J07.0159.01

[5] Remarque sur les nombres de Bernoulli et les nombres d'Euler, Sitz. Kgl. Böhmischen Gesells. Wiss., Prag, (1894), no. 37, 1-4.
J25.0411.02

[6] Sur la fonction $\log \Gamma (a)$, J. Reine Angew. Math., 115 (1895), 201-208.
J26.0474.01

[7] Sur les nombres de Bernoulli, Mathesis (2), 5 (1895), suppl. 2, 1-7.
J26.0285.01

HERMITE CH.: see also SONIN N.YA., HERMITE CH.

HERSCHEL J.F.W.,
[1] On the development of exponential functions, together with several new theorems relating to finite differences, Philos. Trans. Royal Soc. London 104 (1814), 440-468; [2] A Collection of examples of the calculus of finite differences, Cambridge, 1820.

HIDA H.,
[1] A p-adic measure attached to the zeta functions associated with two elliptic modular forms. II. Ann. Inst. Fourier, 38 (1988), no. 3, 1-84.
Z645.10028; M89k:11120

[2] Elementary theory of $L$-functions and Eisenstein series. London Mathematical Society Student Texts, 26. Cambridge University Press, Cambridge, 1993. xii+386 pp.
Z942.11024; M94j:11044

HIGGINS J.,
[1] Double series for the Bernoulli and Euler numbers, J. London Math. Soc., (2) 2 (1970), 722-726.
Z215.33004; M43#147; R1972,2V304

HILBERT D.,
[1] Die Theorie der algebraischen Zahlkörper, Jahresber. Deutsch. Math.-Verein., 4 (1897), 175-546.
J28.0157.05

HILL C.J.D.,
[1] När äro de $n$ forsta termerno af Bernoullis serie gifven funktion af den i den sista ingäende derivatan: Öfversigt Kgl. Vetens.-Akad. Förhandl., Stockholm, 14 (1857), (1858), 259-261.

HIRZEBRUCH F.: see EBBINGHAUS H.-D. et al.

HLAWKA E., SCHOISSENGEIER J., TASCHNER R.,
[1] Geometric and Analytic Number Theory, Springer-Verlag, Berlin etc., 1991, x+238 pp..
Z749.11001; M92f:11002

HOFFMAN M. E.,
[1] Multiple harmonic series, Pacific J. Math., 152 (1992), no. 2, 275-290.
Z763.11037; M92i:11089; R1993,1A103

[2] Derivative polynomials for tangent and secant, Amer. Math. Monthly 102 (1995), no. 1, 23-30.
Z834.26002; M95m:26003

[3] Derivative polynomials, Euler polynomials, and associated integer sequences, Electron. J. Combin. 6 (1999), no. 1, Research Paper 21, 13 pp. (electronic)
M 2000c:11027

HOFSTETTER P.,
[1] Die Bernoullische Funktion und die Gammafunktion, Dissertation, Bern, 1911, 108 pp.
J43.0534.04

HOGGATT V.E.: see ARKIN J., HOGGATT V.E.

HOLDEN J.,
[1] Irregularity of prime numbers over real quadratic fields. Algorithmic number theory (Portland, OR, 1998), 454-462, Lecture Notes in Comput. Sci., 1423, Springer, Berlin, 1998.
M2000m:11113

[2] Comparison of algorithms to calculate quadratic irregularity of prime numbers. Math. Comp. 71 (2002), no. 238, 863-871.

HOLVORCEM P. R.,
[1] Laurent expansions for certain functions defined by Dirichlet series, Aequationes Math., 45 (1993), no. 1, 62-69.
Z770.30004; M93k:30005

HOLZAPFEL R.-P.,
[1] Zeta dimension formula for Picard modular cusp forms of neat natural congruence subgroups, Abh. Math. Sem. Univ. Hamburg 68 (1998), 169-192.
Z945.11011; M2000b:11054

HONG SHAOFANG,
[1] Notes on Glaisher's congruences, Chinese Ann. Math. Ser. B 21 (2000), no. 1, 33-38.
M2001e:11007

HONG SHAO-FANG: see also SUN Qi, HONG SHAO-FANG

HORADAM A. F.,
[1] Genocchi Polynomials, Proc. of the Fourth International Conference on Fibonacci Numbers and Their Applications. Kluwer, Dordrecht, 1991, 145-166.
Z749.11019; M93i:11027

[2] Negative Order Genocchi Polynomials, Fibonacci Quart., 30 (1992), no. 1, 21-34.
Z749.11020; M93a:11016

[3] Generation of Genocchi polynomials of first order by recurrence relations, Fibonacci Quart., 30 (1992), no. 3, 239-243.
Z770.11015; M94e:05012

HORADAM A.F., SHANNON A.G.,
[1] Ward's Staudt-Clausen problem, Math. Scand., 39 (1976), no. 2, 239-250 (1977).
Z347.10010; M56#5411; R1978,5A78

HORADAM A.F.: see also MAHON BR. J.M., HORADAM A.F.

HORATA K.,
[1] An explicit formula for Bernoulli numbers, Rep. Fac. Sci. Technol., Meijo Univ., 29 (1989), no. 1, 1-6.
Z671.10008

[2] On congruences involving Bernoulli numbers and irregular primes, I. Rep. Fac. Sci. Technol., Meijo Univ., 30 (1990), 1-9.
R1991,2A167

[3] On congruences involving Bernoulli numbers and irregular primes, II. Rep. Fac. Sci. Technol., Meijo Univ., 31 (1991), 1-8.
Z856.11009; R1991,12A72

[4] On congruences involving Bernoulli numbers and irregular primes. III. Rep. Fac. Sci. Technol., Meijo Univ., 32 (1992), 15-22.
Z856.11010; R1993,5A168

HORNER J.,
[1] On the forms of $\Delta^{n}0^x$ and their congeners, Quart. J. Math., 4 (1861), 111-123; 204-220.

HOWARD F.T.,
[1] A sequence of numbers related to the exponential function, Duke Math. J., 34 (1967), 599-615.
Z189.04204; M36#130; R1968,6V312

[2] Some sequences of rational numbers related to the exponential function, Duke Math. J., 34 (1967), 701-716.
Z189.04205; M36#131

[3] Properties of the van der Pol Numbers and polynomials, J. Reine Angew. Math., 260 (1973), 35-46.
Z254.10013; M47#6603

[4] Roots of the Euler polynomials, Pacific J. Math., 64 (1976), no. 1, 181-191.
Z331.10005; M54#5444; R1977,4V445

[5] Numbers generated by the reciprocal of $e^x-x-1$, Math. Comp., 31 (1977), no. 138, 581-598.
Z351.10010; M55#12627

[6] A theorem relating potential and Bell polynomials, Discrete Math., 39 (1982), no. 2, 129-143.
Z478.05008; M84e:05015; R1982,10V455

[7] Integers related to the Bessel Function $J_1(z)$, Fibonacci Quart., 23 (1985), no. 3, 249-259.
Z578.10016; M88b:11010; R1986,4A111

[8] Extensions of congruences of Glaisher and Nielsen concerning Stirling numbers, Fibonacci Quart., 28 (1990), no. 4, 355-362.
Z726.11012; M92i:11028; R1991,8V320

[9] The van der Pol numbers and a related sequence of rational numbers, Math. Nachr., 42 (1969), 89-102.
Z208.05401; M41#3385

[10] Generalized van der Pol numbers, Math. Nachr., 44 (1970), 181-191.
Z194.07302; M45#8600

[11] Polynomials related to the Bessel functions, Trans. Amer. Math. Soc., 210 (1975), 233-248.
Z308.10008; M52#253; R1976,4B45

[12] Factors and roots of the van der Pol polynomials, Proc. Amer. Math. Soc., 53 (1975), no. 1, 1-8.
Z313.10011; M52#252; R1976,7V375

[13] A special class of Bell polynomials, Math. Comp., 35 (1980), no. 151, 977-989 .
Z 438.10012; M82g:10028; R1981,4V377

[14] Nörlund's number $B_n^{(n)}$. Applications of Fibonacci Numbers, Vol. 5 (G. E. Bergum et al., Eds.), 355-366, Kluwer Acad. Publ., Dordrecht, 1993.
Z805.11023; M95e:11029

[15] Congruences and recurrences for Bernoulli numbers of higher order. Fibonacci Quart., 32 (1994), no. 4, 316-328.
Z820.11009; M95k:11021

[16] Applications of a recurrence for Bernoulli numbers, J. Number Theory, 52 (1995), no. 1, 157-172.
Z805.11023; M96e:11027

[17] Formulas of Ramanujan involving Lucas numbers, Pell numbers, and Bernoulli numbers. In: G.E. Bergum et al. (eds.), Applications of Fibonacci Numbers, Vol. 6, 257-270. Kluwer Acad. Publ., Dordrecht, 1996.
Z852.11007; M97d:11039

[18] Explicit formulas for degenerate Bernoulli numbers, Discrete Math., 162 (1996), no. 1-3, 175-185.
Z873.11016; M97m:11024

[19] Sums of powers of integers via generating functions, Fibonacci Quart., 34 (1996), no. 3, 244-256.
Z859.11016; M98a:11025; R1997,10A200

[20] Lacunary recurrences for sums of powers of integers, Fibonacci Quart., 36 (1998), no. 5, 435-442

[21] A general lacunary recurrence formula. Applications of Fibonacci numbers. Vol. 9, 121-135, Kluwer Acad. Publ., Dordrecht, 2004.
Z1064.11007; M2005e:11026

HSU L. C. [XU LI ZHI],
[1] Power-type generating functions. Approximation theory (Kecskemét, 1990), 405-412. Colloq. Math. Soc. János Bolyai, 58, North-Holland, Amsterdam, 1991.
Z768.41030; M94g:41054

[2] Finding some strange identities via Faa di Bruno's formula, J. Math. Res. Exposition 13 (1993), no. 2, 159-165.
Z783.05006; M94f:05007

HSU L.C., CHU W.,
[1] A kind of asymptotic expansion using partitions. Tôhoku Math. J., 43 (1991), no.2, 235-242.
Z747.41030; M92g:41038

HUANG I-CHIAU, HUANG SU-YUN,
[1] Bernoulli numbers and polynomials via residues, J. Number Theory, 76 (1999), no. 2, 178-193.
Z940.11009; M2000d:11027

HURWITZ A.,
[1] Einige Eigenschaften der Dirichlet'schen Functionen $\Gamma (s) = \sum (D/n){1/n^s}$, die bei der Bestimmung der Classenzahlen binärer quadratischer Formen auftreten, Zeitsch. für Math. und Physik, 27 (1882), no. 1, 86-101.
J14.0371.01

[2] Über die Anzahl der Klassen binärer quadratischer Formen von negativer Determinante, Acta Math., 19 (1895), 351-384.
J26.0226.03

[3] Über die Entwicklungscoefficienten der lemniscatischen Functionen, Math. Ann., 51 (1898), 196-226.
J29.0385.02

[4] Über die Entwickelungscoefficienten der lemniskatischen Functionen. Nachr. Kgl. Ges. Wiss. Göttingen, (1897), 273-276.
J28.0393.01

HUSSAIN M.A., SINGH S.N.,
[1] On generalized polynomial set $D_n(x;a,k)$, Indian J. Pure Appl. Math., 9 (1978), no. 11, 1158-1162.
Z402.33007; M80b:10018; R1979,4B52

HUTCHINSON J.I.,
[1] On the roots of the Riemann zeta function, Trans. Amer. Math. Soc., 27 (1925), 49-60.
J51.0267.01; J51.0271.09


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