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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
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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 .
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[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.
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[17] Formulas of Ramanujan involving Lucas numbers, Pell numbers, and
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[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
[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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