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 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: INTEGRALS OF BESSEL FUNCTIONS 491 [11.12] V. R. Bursian and V. Fock, Table of the functions Akad. Nauk, Leningrad, Inst. Fiz. Mat., Trudy (Travaux) 2, 6-10 (1931). SmKo(t)dt, z=O(.1)12, 7D; ez Ko(t)dt, z=0(.1)16, 7D; e-2 [ ~ o ( t ) d t , z= so” Io(t)dt, z=0(.1)6, 7D; 0 (.1)16, 7D. [11.13] E. A. Chistova, Tablitsy funktsii Besselya ot deistvitel’ nogo argumenta i integralov ot nikh (Izdat. Akad. Nauk SSSR., MOSCOW, U.S.S.R., 1958). J,(z), Y,(z), Sm dt, Lm dt, n=O, 1; z=0(.001)15(.01)100, 7D. Also tabulated are auxiliary expressions to facil- itate interpolation near the origin. [11.14] A. J. M. Hitchcock, Polynomial approximations to Bessel functions of order zero and one and to related functions, Math. Tables Aids Comp. 11, 86-88 (1957). Polynomial approximations for i2 Jo(t)dt and LWKdt)dt. [11.15] C. W. Horton, A short table‘ of Struve functions and of some integrals involving Bessel and Struve functions, J. Math. Phys. 29, 56-58 (1950). C,(z) =r tnJ,(t)dt, n=l(1)4,z=O(.l) 10, 4D; D,(z) =S’ tnE,(t)dt, n=0(1)4, z=0(.1)10, 4D, where H,(z) is Struve’s function; see chapter 12. [11.16] J. C. Jaeger, Repeated integrals of Bessel functions and the theory of transients in filter circuits, J. Math. Phys. 27, 210-219 (1948). f~(z)= so2 Jo(t)dt, f&) =S2f,-l(0& 2-%(z), r=1(1)7, z=0(1)24, 8D. Also %(z) =S J0[2(zt)’W,(t)dt, an@), @i(z), n=1(1)7, z=0(1)24, 4D. [11.17] L. N. Karmazina, and E. A. Chistova, Tablitsy funktsii Besselya ot mnimogo argumenta i integralov ot nikh (Izdat. Akad. Nauk SSSR., MOSCOW, U.S.S.R., 1958). e-.lo(z), e-zZl(z), eZKo(z), ezKl(z), ez, e-zs,’ ~o(t)dt, ezJzm ~ o ( t ) d t , z=0(.001)5(.005)15(.01)100, 7D except for e8 which is 75. Also tabulated are auxiliary expres- sions to facilitate interpolation near the origin. Lm 0 m [11.18] H. L. Knudsen, Bidrag ti1 teorien for antenne- systemer med he1 eller delvis rotations-symmetri. I (Kommission Has Teknisk Forlag, Copenhagen, Denmark, 1953). J,(t)dt, n=0(1)8, z= 0(.01)10, 5D. Also J,(t)eW,a=t, a=s-t. [11.19] Y. Z. Luke and D. Ufford, Tables of the function RO(Z) =s,’K~(t)dt. Math. Tables Aids Comp. UMT 129. T?o(z)=-[r+ln (z/2)]A1(z)+Aa(z), lo(z)dz and femKo(z)dz, Roy. SOC. Unpublished Math. Table File No. 6. a=0(.02)2(.1)4, 9D. [11.21] G. M. Muller, Table of the function s,’ s,’ A,(\$), Aa(z). ~=0(.01).5(.05)1, 8D. [11.20] C. Mack and M. Castle, Tables of .r Kj,(z) =z-ns,’unKo(u) du, Office of Technical Services, U.S. Department of Commerce, Washington, D.C. (1954). n=O( 1) 31, z = O( .01) 2( .02) 5, [11.22] National Bureau of Standards, Tables of functions and zeros of functions, Applied Math. Series 37 (U.S. Government Printing Office, Washington, D.C., 1954). (1) pp. 21-31: s,’Jo(t)dt, s,’ Y~(t)dt, 8s. ~=0(.01)1O, 1OD. (2) pp. 33-39: Jo(t)dt/t, s=0(.1)10(1)22, 10D; F ( z ) = S m Jo(t)dt/t +ln (2/2), z=0(.1)3, 10D; P ) ( z ) / n ! , x= 10(1)22, n=0(1)13, 12D. [ 11.231 National Physical Laboratory, Integrals of Bessel functions, Roy. SOC. Unpublished Math. Table r [11.24] M. Rothman, Table of Io(z)dz for 0(.1)20(1)25, Quart. J. Mech. Appl. Math. 2, 212-217 (1949). 8s-9s. Jo(t)dt for large z, J. Math. Phys. 34, 169-172 (1955). z=10(.2)40, 6D. [11.26] G. N. Watson, A treatise on the theory of Bessel functions, 2d ed. (Cambridge Univ. Press, Cam- bridge, England, 1958). Table VIII, p. 752: kPo(t)dt, is,’Yo(t)dt, z=0(.02)1, 7D, with the first 16 maxima and minima of the integrals to 7D. s,’ [11.25] P. W. Schmidt, Tables of s,’ 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.