New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | SMALL | MEDIUM | LARGE Below is the OCR-scanned text from this page: 9 . Bessel Functions of Integer Order F . W . J . OLVER~ Contents Page Mathematical Properties . . . . . . . . . . . . . . . . . . . . 358 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 Bessel Functions Jand Y . . . . . . . . . . . . . . . . . . . 358 9.1. Definitions and Elementary Properties . . . . . . . . . 358 9.2. Asymptotic Expansions for Large Arguments . . . . . . 364 9.3. Asymptotic Expansions for Large Orders . . . . . . . . 365 9.4. Polynomial Approximations . . . . . . . . . . . . . . 369 9.5. Zeros . . . . . . . . . . . . . . . . . . . . . . . . 370 374 374 9.7. Asymptotic Expansions . . . . . . . . . . . . . . . . 377 9.8. Polynomial Approximations . . . . . . . . . . . . . . 378 Kelvin Functions . . . . . . . . . . . . . . . . . . . . . . . 379 379 9.10. Asymptotic Expansions . . . . . . . . . . . . . . . 381 9.11. Polynomial Approximations . . . . . . . . . . . . . 384 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . 385 9.12. Use and Extension of the Tables . . . . . . . . . . . 385 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 Table 9.1. 390 Modified Bessel Functions I and K . . . . . . . . . . . . . . . 9.6. Definitions and Properties . . . . . . . . . . . . . . 9.9. Definitions and Properties . . . . . . . . . . . . . . Bessel Functions-Orders 0. 1. and 2 (0 525 17.5) . . . . Jo(x). 15D, Ji(x). Jz(x). Yo(.), Yi(2). 10D Yz(z). 8D ~=0(.1)17.5 Bessel Functions-Modulus and Phase of Orders 0, 1. 2 ( 1 0 5 s 5 m ) . . . . . . . . . . . . . . . . . . . . 396 x*Mn(x). 0, (x) -5. 8D 72= 0 (1)2. 2-1= . 1 (- . 0 1) 0 Bessel Functions-Auxiliary Table for Small Arguments (05x52) . . . . . . . . . . . . . . . . . . . . . 397 2 2 Yo(z)-; Jo(z) In x. z[Y1(x)-; Jl(z) In 21 2=0(.1)2, 8D Table 9.2. Bessel Functions-Orders 3-9 (0 5x520) . . . . . . . . 398 J m (5) . y7z (4 . 2= O( .2)20. n=3 (1)9 5D or 5s 1 National Bureau of Standards. on leave from the National Physical Laboratory . 355 ~~ ~~ - The page scan image above, and the text in the text box above, are contributions of the National Institute of Standards and Technology that are not subject to copyright in the United States.