Transcript Document

A New Handbook and Web Site of
Properties of Special Functions
Dan Lozier
NIST
IMA Workshop
Special Functions in the Digital Age
July 22, 2002
Impact of NBS Handbook
• Sales
– Government edition >150,000
– Commercial editions ~500,000
• Citations (SCI)
– approaching 1500/yr recently
– cited about every 1.5 hours
• Citing journals
– primarily physical science, engineering
Milton Abramowitz
1915-1958
Irene Stegun
1919-
NBS Handbook Obsolescence
• Math research since 1960
• Computer developments since 1960
Impact of Computers
• Tables are dead!
– Fortran I (1954 - 57)
– IMSL & NAG (1970 - 71)
• Formulas in books are dying! (maybe)
– Macsyma (1969)
– TeX (1977)
– MathML, OpenMath, …, MKM
Mathematical Knowledge Management
• Formalism vs. Intuitionism
• Formal vs. informal proof
• Computers can make formal proofs
possible! (maybe)
• Encode semantics, not just syntax
• Encode proof techniques
DLMF Approach
Mathematics Database
DLMF Handbook
DLMF Web Site
Other DLMF Documents (future)
DLMF Database
• Collection of computer files
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AMS-Latex
PostScript
VRML
MathML (future)
• Basis for generating DLMF documents
• Constructed, maintained at NIST
Audience for DLMF Documents
• Experienced scientific professionals
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Physicists, other scientists
Engineers
Statisticians
Mathematicians, esp. applied
• Trainers and teachers (future)
DLMF Handbook
• Model: NBS Handbook
– Large pages
– Double-column
– 1000 pages
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Color graphics
Produced by NIST
Marketed by a commercial publisher
Low price
DLMF Handbook Content
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Validated math properties
Sample applications
Computation
Chapters on individual functions
Chapters on methodology
References
Indexes
DLMF Handbook Style
• Model: NBS Handbook
– concise
– oriented to users of special functions
• Start with specifics, move to general
• Not traditional math style
• Not pedagogical
DLMF Web Site
• DLMF Handbook content plus
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software references & downloading
search engine
dynamic graphics
formula downloading
• Constructed, maintained by NIST
– latex2html
– free access
Timetable
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Conception
Sample chapter, Web prototype, NSF proposal
NSF funding received
Authors identified, chapter outlines received
Chapters received and edited
Chapters received, revised, edited, validated
Book published, Web site announced
NIST Editors
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General - Dan Lozier
Mathematics - Frank Olver
Physics – Charles Clark
Information Technology – Ron Boisvert
Associate Editors
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Special Functions – Dick Askey, Nico Temme
Physics – Michael Berry, Leonard Maximon
Chemistry – Bill Reinhardt
Numerical Analysis – Walter Gautschi
Combinatorics – Morris Newman
Computer Algebra – Peter Paule
Statistics – Ingram Olkin
Chapters 1-7
(Subject to change.)
MP. Mathematical and Physical Constants — C. Clark
AL. Algebraic and Analytical Methods — R. Askey, F. Olver, R. Roy
AS. Asymptotic Approximations — F. Olver, R. Wong
NM. Numerical Methods — W. Gautschi, C. Brezinski
CA. Computer Algebra — P. Paule, F. Chyzak
EF. Elementary Functions — R. Roy, P. Turner, S. Krantz
GA. Gamma Function — R. Askey, R. Roy
Chapters 8-13
EX. Exponential, Logarithmic, Sine and Cosine Integrals — N. Temme
ER. Error Functions, Dawson’s and Fresnel Integrals — N. Temme
IG. Incomplete Gamma Functions and Related Functions — R. Paris
AI. Airy and Related Functions — F. Olver
BS. Bessel Functions — F. Olver, L. Maximon
ST. Struve Functions and Related Functions — R. Paris
Chapters 14-20
CH. Confluent Hypergeometric Functions — A. Olde Daalhuis
CW. Coulomb Wave Functions — M. Seaton
PC. Parabolic Cylinder Functions — N. Temme
LE. Legendre Functions & Spherical Harmonics — T.M. Dunster
HY. Hypergeometric Functions — A. Olde Daalhuis
GH. Generalized Hypergeometric Functions — R. Askey, A. Olde
Daalhuis, D. Richards
QH. q-Hypergeometric Functions — G. Andrews
Chapters 21-27
CP. Classical Orthogonal Polynomials — T. Koornwinder,
R. Koekoek, R. Swarttouw
OO. Other Orthogonal Polynomials — T. Koornwinder,
R. Koekoek, R. Swarttouw
EL. Elliptic Integrals — B. Carlson
TH. Theta Functions — P. Walker, W. Reinhardt
MT. Riemann Theta Functions — B. Deconinck
JA. Jacobian Elliptic Functions — P. Walker, W. Reinhardt
WE. Weierstrass Elliptic and Modular Functions — P. Walker,
W. Reinhardt
Chapters 28-34
BP. Bernoulli and Euler Numbers and Polynomials — K. Dilcher
ZE. Zeta and Related Functions — T. Apostol
CM. Combinatorial Analysis — D. Bressoud
NT. Functions of Number Theory — T. Apostol
SM. Probability and Statistical Distributions and Functions
— I. Olkin, N. Sedransk, D. Kemp.
MA. Mathieu Functions and Hill’s Equation — G. Wolf
LA. Lame Functions; Spheroidal Wave Functions — H. Volkmer
Chapters 35-40
SW. Spheroidal Wave Functions — H. Volkmer
HE. Heun Functions — B. Sleeman, V. Kuznetsov
PT. Painleve Transcendents — P. Clarkson
IC. Integrals with Coalescing Saddles — M. Berry, C. Howls
TJ. 3j, 6j, 9j Symbols — L. Maximon
RN. Random Numbers — G. Marsaglia, G. Casella
DLMF Handbook Mockup
..\..\DLMF\docs\book.ps
3 Early Examples of
Research Stimulated by DLMF
• Jacobian elliptic functions: For fixed z,
what is the behavior of sn(z,k), cn(z,k), ...
for complex k?
• Euler dilogarithm of complex argument
• Elliptic integrals (Carlson’s form):
improvement of algorithms for computation
NIST Staff
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Information Architect – Bruce Miller
Graphics – Bonita Saunders, Qiming Wang
Search Engine – Abdou Youssef (GWU)
Web Site – Joyce Conlon, Marje McClain
Statistics Consultant – Raghu Kacker
Algorithms – Bruce Fabijonas (SMU)
Students – Brianna Blaser, Elaine Kim, Dan
Cardy, Stuart Fletcher, Grace Chu
NIST Funding
• Covers all internal, some external costs
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IT Lab (1997 - )
Physics Lab (1997 - )
Standard Reference Data (1997 - )
Manufacturing Engineering Lab (98 - )
Advanced Technology Program (99 – 00)
NSF Funding
• Covers only external costs
– Authors contracts
– Validators contracts
– Associate editors costs
• Source: KDI Program
• Administered by DMS
• Received September 1999 (3 years + 1)
Author’s Contracts
• Deliverables
– Outline
– Acceptable draft
– Final draft
• Copyright transfer required
• Detailed instructions provided
Validator’s Contracts
• Purpose: verify all mathematics
• Deliverable: Validation report
DLMF Public Web Site
http://dlmf.nist.gov