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SEMINARIO MATEMATICO Università' e Politecnico Torino

Fascicoli speciali pubblicati in anni precedenti

Stochastic Problems in Mechanics Linear Partial and Pseudo Differential Operators Differential Geometry on Homogeneous Spaces

Distribuzione in Italia ROSENBERG & SELLIER, Editori in Torino Via Andrea Doria, 14 10123 TORINO

Abbonamento 1985 (3 Fascicoli ordinari e 1 speciale) Fascicolo speciale

Italia

100.000

50.000

Europa Extraeuropa

135.000 190.000

70.000 90.000

Inviare assegno bancario sbarrato o effettuare versamento sul ccp 11571106 intestato a Rosenberg & Sellier Editori in Torino, specificando la causale del versamento: «Rendiconti del Seminario Mate­matico, abbonamento 1985» Le annate arretrate si vendono al prezzo dell'abbonamento in corso. Per abbonamenti, cambi di indi­rizzi, informazioni scrivere a Rosenberg.

C O M I T A T O DI R E D A Z I O N E

Triennio 1981 - 1984

F. FAVA (Direttore), S. NOCILLA e F. SKOF (vice-Direttori),

A. CONTE, M. FRANCAVIGLIA, L. GATTESCHI, G. LOLLI,

G. MONEGATO, F. RICCI, P. VALABREGA

Segretaria: L. PICCO BOTTA

FASCICOLO SPECIALE OTTOBRE 1984

RENDICONTI DEL

SEMINARIO MATEMATICO

Convegno su

«SPECIAL FUNCTIONS: THEORY AND COMPUTATION»

TORINO, 10-12 ottobre 1984

UNIVERSITÀ' E POLITECNICO TORINO

Proprietà Letteraria Riservata

PREFACE

This special issue of the "Rendiconti del Seminario Matematico dell'Uni­versità e del Politecnico di Torino" contains, in complete form, the texts of the lectures delivered by the invited speakers at the "International Conference on Special Functions: Theory and Computation", held in Turin from the lOth totbe 12th of October 1984, as one of the activities of the Seminano Matematico.

The aim of the Conference was to bring togethcr expcrts in various ficlds of special functions in ordcr to cxchange ideas and discuss currcnt problcms. We have got a mixed audience of about onc hundrcd Mathcmaticians and Physicists, coming from academic and industriai communities.

Itis withgreat plcasure that we thank the participants, the speakers, the sponsors: Consiglio Nazionale delle Ricerche, Regione Piemonte, Toro Assi­curazioni, Olivetti Computers.

A particular thank to P. Baratella and R. Besenghi, for the locai organi-zation of the Conference and to B. Gabutti, G. Pittaluga, C. Giordano, L. Sa­cripante for their valuable hclp.

July 1985 The organizing commitee

G. Allasia L. Gatteschi W. Gautschi G. Monegato

C O N T E N T S

Preface.

Names and Addresses of Invited Speakers.

List of Participants.

Programme.

Pag. V

IX

XI

XIII

CONFERENCES

R. Askey, Some problems about special functions and computations.

F. Calogero, Some applications of a e onvenient finite-dimensionai matrix representation of the differential operator.

B. C. Carlson, The hypergeometric function and the R-function near their branch points.

W.J. Cody, Software for special functions.

C.L.Frenzen, R. Wong, The Lebesgue constants for Jacobi series.

L. Gatteschi, On the zeros ofjacobi polynomials and Bessel functions.

W. Gautschi - G.V. Milovanovic, Polynomials orthogonal on the se michele.

K.S. Kòlbig, Some problems involving special functions arising from Physicsat CERN.

P.G. Nevai, Orthogonal polynomials on infinite intervals.

F.W.J. Olver, Unrestricted algorithms for mathematical functions,

R. Piessens - M. Branders, A survey of numerical methods for the

computation of Bessel function integrals.

W. Schempp, Theta identities via Laguerre functions - a nilpotent

harmonic analysis approach.

pag.

23

63

91

117

149

179

187

215

237

249

267

Vili

N.M. Temme, Special functions as approximants in uniform asymptotic expansions of integrals; a survey. Pag. 289

j.Wimp,Multidimensional iteration algorithms, "' 319

NAMES AND ADDRESSES OF INVITED SPEAKERS

RICHARD A. ASKEY, Department of Mathematics, University of Wisconsin, Van Vleck Hall, Madison, WI 53706, U.S.A.

FRANCESCO CALOGERO. Dipartimento di Fisica, Università degli Studi "La Sapienza", Piazzale Aldo Moro 2, 00185 Roma, Italy.

BILLE C. CARLSON. Ames Laboratory and Department of Mathematics, Iowa State Uni­versity, Ames, Iowa 50011, U.S.A.

WILLIAM J. CODY. Mathematics and Computer Science Division, Argonne National Labo­ratory, Argonne, IL 60439, U.S.A.

LUIGI GATTESCHI. Dipartimento di Matematica dell'Università - V. Carlo Alberto, 10-10123 Torino, Italy.

WALTER GAUTSCHI. Department of Computer Sciences, Purdue University, West Lafa-yette, IN 47907, U.S.A,

KURT SIEGFRIED KÒLBIG. CERN, CH 1211 Genève 23, Switzerland.

PAUL G. NEVAI. Ohio State University, Columbus, OH 43210, U.S.A.

FRANK W. J. OLVER. Department of Mathematics, Institute for Physycal Science and Technology, University of Maryland, College Park, MA 20742, U.S.A.

ROBERT PIESSENS. Department of Computer Science, Catholic University of Leuven,Ce-lestijnenlaan 200A, B-3030 Heverlee, Belgium.

WALTER SCHEMPP. Lehrstuhl fuer Mathematik I, University of Siegen, D-5900 Siegen, Federai Republic of Germany, NICO M. TEMME.. Department of Applied Mathematics, Centre for Mathematics and Com­puter Science, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands.

JET WIMP. Department of Mathematics, Drexel University, Philadelphia, PA 19104, U.S.A.

RODERICK WONG. Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.

LISTOF PARTICIPANTS

GIAMPIETRO ALLASIA, Univ. Torino, Italy; ALDO ASCARI, Univ. Parma, Italy, PAOLA BARATELLA, Univ. Torino, Italy; VITTORIO BARBERIO, Olivetti Torino, Italy,GIUSEPPE BARUCCHI, Univ. Torino, Italy; LUCILLA BASSOTTI RIZZA, Univ. Parma, Italy; SERGIO BENENTI, Univ. Torino, Italy; RENATA BESENGHI, Univ. Torino, Italy; CLAUDIA BIGNOLI, Fiat Torino, Italy; W.G.C. BOYD, Univ. Bristol, England; MIRA BOZZINI, Univ. Milano, Italy? FRANCO BRESSAN, Univ. Verona, Italy; MARIA LUISA BUZANO, Univ. Torino, Italy; FRANCA CALIO', Polit. Milano, Italy; RENATO CAMPO, C.S.E.L.T. Torino, Italy; NISIDA CERA, Univ. Pescara, Italy; CESARE CHICCOLI, L.N.A.F.-I.N.F.N. Bologna, Italy; MARCO CODEGONE, Polit. Torino, Italy-, ALBERTO CONTE, Univ. Torino, Italy; GIULIANA CRISCUOLO, I.A.M.-C.N.R. Napoli, Italy; CATERINA DAGNINO, Polit. Torino, Italy; ALESSANDRA D'ALESSIO, Univ. Napoli, Italy-, DOMENICO DELBOSCO, Univ. Torino, Italy; VITTORIA DEMICHELIS, Univ. Torino, Italy; FLAVIA DE TISI, Univ. Milano, Italy; MAURO DILIGENTI, Univ. Torino, Italy; MICHELE ELIA, Polit. Torino, Italy; FRANCO FAVA, Univ. Torino, Italy; EZIO FERRARI, Univ. Roma, Italy; GIUSEPPE FIGLIA,C.S.E.L.T. Torino, Italy; MARGHERITA FOCHI, Univ. Torino, Italy; MARCO FRONTINI, Polit. Milano, Italy; DANIELE FUNARO, Univ. Pavia, Italy; BRUNO GABUTTI, Univ. Torino, Italy; GIOVANNI G ALATI OTO,Toro Ass. Torino, Italy ; MARI A TERESA GALIZIA, Polit. Torino, Italy: CARLA GIORDANO, Univ. Torino, Italy; LAURA CORI, Univ. Roma, Italy; LAURA GOTUSSO, Polit. Milano, Italy; BRUNA TIRA GRISERI, Univ. Torino, Italy; LIANA GUERCIA, Univ. Lecce, Italy; TAKESHI KANO, Univ. Okayama, Japan-, GIULIANO LACETTI, Univ. Napoli, Italy-, ANDREA LAFORGIA, Univ. Torino, Italy; LICIALENARDUZZI.I.A.M.I.-C.N.R.Milano, Italy; FRANCESCO LERDA, Univ. Torino, Italy; SILVERIA LORENZUTTA, E.N.E.A. Bologna, Italy; MARIA MASCARELLO, Polit. Torino, Italy; GIUSEPPE MASTROIANNI, I.A.M.-C.N.R. Napoli, Italy; MARIA LUISA MATHIS, Univ. Torino, Italy; BRUNO MINETTI, Polit. Torino, Italy; GIOVANNI MONEGATO, Polit. Torino, Italy; MARIA MORANDI CECCHI, Univ. Padova, Italy; CESARE MORETTI, Toro Ass. Torino, Italy; PAOLA MORONI, Polit. Torino, Italy; MARTIN MULDOON, Univ. York, Canada-, ALMERIGO MURLI, Univ. Napoli, Italy; SILVIO NOCILLA, Polit. Torino, Italy; ANNA MARIA ORSI PALAMARA, Polit. Torino, Italy; MIRIAM PANDOLFI, Polit. Torino, Italy; FRANCO PASTRONE, Univ. Torino, Italy-,

XIV

THURS DAY, October 11

Morhing

Chairman: Prof. B.C. CARLSON

9.00-10.00 F.W.J. OLVER - Unrestricted algorithms for mathematical functions. 10.00-11.00 J. W1MP - Multidimensional iteration algorithms. 12.00-13.00 W.J. CODY -Software for special functions.

Afternoon

Chairman: Prof. F.W.J. OLVER

14.30-15.30 K.S. KOLBIG - Some problems involving special functions arising from Physics at CERN.

15.30-16.30 R. PIESSENS - A survey of numerical methods for the computation of Bessel functions integrals.

17.00-17.30 L. GATTESCHI - On the zeros of Jacobi polynomials and Bessel func­tions.

20.00 Informai dinner.

FRI DAY, October 12

Morning

Chairman: Prof. R. WONG

9.00-10.00 B.C. CARLSON - The hypergeometric function and the R-function near their branch points.

10.00-11.00 W. SCHEMPP - Theta identities via Laguerre-Weber functions - a nilpotent harmonic analysis approach.

12.00-13.00 F. CALOGERO - Some applications of a convenient finite-dimensional màtrix representation of the differential operator.

SPECIAL FUNCTIONS: THEORY AND COMPUTATION

Finito di stampare nel mese di novembre 1985 presso "LA PRECISA"

Via M. Gioia, 3 - TORINO

INDICAZIONI PER GLI AUTORI

I lavori destinati alla pubblicazione sui Rendiconti del Seminario Mate­

matico dell'Università e del Politecnico di Torino devono essere inviati in du­

plice copia al seguente indirizzo:

Seminario Matematico dell'Università e del Politecnico di Torino Via Carlo Alberto 10 10123 Torino

I lavori presentati devono essere dattiloscrìtti e una delle due copie deve contenere le eventuali indicazioni per il tipografo.

I lavori devono essere inoltre completi di bibliografia e corredati della classificazione AMS.

Gli autori riceveranno gratuitamente 50 estratti per ogni articolo. Even­tuali richieste di ulteriori estratti a pagamento devono essere presentate all'at­to della restituzione delle prime bozze.

Di regola le seconde bozze non vengono inviate agli autori per la corre­zione.

ISSN 0373-1243