1. NA-MKM 2004 Phoenix MKM and the NIST DLMF Dan Lozier National Institute of Standards and Technology Gaithersburg, MD 20899-8910

2. KM and MKMNA-MKM 2004 Phoenix2 Traditional Methods of KM Handbooks, dictionaries, encyclopedias, atlases Springer-NY search: Keyword “handbook”: 1125 hits “Handbook” in title/subtitle: 802 hits CRC Press search: “Handbook” in title/subtitle, “mathematics” as subject/discipline: 41 hits

3. KM and MKMNA-MKM 2004 Phoenix3

4. KM and MKMNA-MKM 2004 Phoenix4

5. KM and MKMNA-MKM 2004 Phoenix5

6. KM and MKMNA-MKM 2004 Phoenix6

7. KM and MKMNA-MKM 2004 Phoenix7

8. KM and MKMNA-MKM 2004 Phoenix8 New Methods of KM for Math Stimulus: –CD/DVD, web sites, “digital technology” –Interactive graphics (scientific visualization) –Computer algebra, theorem provers Key research areas –Math notation and definition –Presentation/representation of math –Math-aware search –Hardware/software standards –Formal methods

9. DLMFNA-MKM 2004 Phoenix9 NIST Digital Library of Mathematical Functions Project 1997 - project conceived 1998 - sample chapter & prototype web site 1999 - NSF funding received 2000 – 2004 Math content development, editing, validation Web development, inc. search & graphics 2005 – book published, web site released

10. DLMFNA-MKM 2004 Phoenix10 Personnel 4 principal editors 10 associate editors 35 authors 25 validators 15 NIST staff

11. DLMFNA-MKM 2004 Phoenix11

12. DLMFNA-MKM 2004 Phoenix12

13. DLMFNA-MKM 2004 Phoenix13 DLMF Web Site Features –Math content –Metadata –Interactive graphics –Math-aware search Demonstration

24. SearchNA-MKM 2004 Phoenix24 DLMF Equation Search System DLMF Database Query Input Query Processing Search Engine Query Output Presentation Module

25. SearchNA-MKM 2004 Phoenix25 Query Expression and Entry Simplified, Latex-like query language Operators & symbols that can be expressed with 1 or 2 keyboard strokes are so entered Otherwise, alphabetical names are used (both full-names and short-hand names) “\” not needed {} and () are equivalent

26. SearchNA-MKM 2004 Phoenix26 Examples OpsEntryOpsEntry Arith ops+ - * /Power, super^ ±,  +-, -+Subscript_ ≤, ≥ =~, ≈~, ~~ ,  =~, =- , not < !=, !< Goes to-> ,  =>, ∫, ∑int, sum∞infinity  nebla√sqrt

27. SearchNA-MKM 2004 Phoenix27 Query Results: 2 Choices 1.Document list –Links to DLMF sections –Matching equations highlighted 2.Equation list Created on-the-fly Links to containing document, positioned with matching equation at top of window

28. SearchNA-MKM 2004 Phoenix28 Recent Developments Mathematica and Maple nomenclature function names order of arguments Wild cards $ matches any one token \* matches any alphanumeric string in a token Null in argument list, e.g. Euler’s generalized beta integral Beta[z0,z1,,]

29. SearchNA-MKM 2004 Phoenix29 DLMF Search Demonstrations Mathematica and Maple Illustrations Equation Search Page

38. Legendre FunctionsNA-MKM 2004 Phoenix38 Legendre Functions

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40. Legendre FunctionsNA-MKM 2004 Phoenix40

41. Legendre FunctionsNA-MKM 2004 Phoenix41

42. Legendre FunctionsNA-MKM 2004 Phoenix42

43. Legendre FunctionsNA-MKM 2004 Phoenix43

44. Legendre FunctionsNA-MKM 2004 Phoenix44

45. Legendre FunctionsNA-MKM 2004 Phoenix45

46. Spheroidal Wave Functions NA-MKM 2004 Phoenix46 Spheroidal Wave Functions

47. NA-MKM 2004 Phoenix47

48. Spheroidal Wave Functions NA-MKM 2004 Phoenix48

49. Spheroidal Wave Functions NA-MKM 2004 Phoenix49

50. Spheroidal Wave Functions NA-MKM 2004 Phoenix50

51. Spheroidal Wave Functions NA-MKM 2004 Phoenix51

52. Spheroidal Wave Functions NA-MKM 2004 Phoenix52

53. Spheroidal Wave Functions NA-MKM 2004 Phoenix53 SW.6 Functions of Complex Argument

54. NA-MKM 2004 Phoenix54 Implications for MKM For a given “family” of SF there exist –many alternative notations –a wide variety of useful definitions –Increased complications when numerical computation is considered We want to be able to move freely among them Real variables are hard enough Complex variables are much harder

55. NA-MKM 2004 Phoenix55 Future Directions at NIST (Complete development of basic content) (Publish book, release initial web site) Improve web site –XML/MathML –Content MathML –Improved search (XQUERY) –Rudimentary, at least, equation equivalences –Tables & graphs “on demand” Possible second edition, possible new subject area