      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: 10. Bessel Functions of Fractional Order H. A. ANTOSIEWICZ~ Con tents Mathematical Properties . . . . . . . . . . . . . . . . . . . . 10.1. Spherical Bessel Functions . . . . . . . . . . . . . . . 10.2. Modified Spherical Bessel Functions . . . . . . . . . . . 10.3. Riccati-Bessel Functions . . . . . . . . . . . . . . . . 10.4. Airy Functions . . . . . . . . . . . . . . . . . . . . Numerical Methods . . . . . . . . . . . . . . . . . . . . . . 10.5. Use and Extension of the Tables . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . Table 10.1. Spherical Bessel Functions-Orders 0, 1, and 2 (0 5x5 10) . j n ( d , Y n ( 4 n=O, 1, 2; x=0(.1)5, 6-8S, \$=5(.1)10, 5s Table 10.2. Spherical Bessel Functions-Orders 3-10 ( 0 ~ ~ ~ 1 0 ) . . . jdd, Y n ( 4 x-njn(4, xnt1Yn(4 n=3(1)8; z=O(.l)lO, 5s n=9, 10; s=0(.1)10, 7-8s Table 10.3. Spherical Bessel Functions-Orders 20 and 21 (0 1x525) . K~ exp (92/(4n+2)ljn(z) Ptl exp (-x22/(4n+2))y,(z) n=20, 21; x=0(.5)25, 6-8s Table 10.4. Spherical Bessel Functions-Modulus and Phase-Orders 9,10,20 and 21 . . . . . . . . . . . . . . . . . . . . . . . &JG+tP), On+t(4--2 where j n ( 4 = I l G m f n + t ( 4 - cos e n + t ( 4 Y n ( 4 = 113~/~Mz+t (.) sin en++ (4 n=9, 10; ~-~=.1(-.005)0, 8D n=20, 21; ~ ~ = . 0 4 ( - - . 0 0 2 ) 0 , 8D j n ( d , Y n ( 4 Table 10.5. Spherical Bessel Functions-Various Orders (0 -