SKEP Integral

SKEP Integral - a"; 4.053 = j .ACEMb) +3?) 5646 17...

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Unformatted text preview: a"; 4.053 = j .ACEMb) +3?) 5646 17 7;“ h h , 1. J. _ E .4. .51 2 (effigywflw z'rr p54"? “a 77' nzc *H Ft 3 6x10 ECGJQDCOJ¢9” Z—Ldeagzéésjqcfis -‘i? -—, .1. _._ ZTT 5 my} 2 C05 (64-?‘531 &¢' 47 Eda/lam. EKWQ W 1T 56) mum (:51 Ms BESSEL FUNCTIONS OF INTEGER ORDER Integral Representations ID(2 :1]: 3*” m“ 9 (30:11: cosh (z (:05 (3)636 11' 9.6.17 mop—lg 61” mi “+16 (2.6 $1193”ch 1T 1:4 v I' _ I.(2)=—£2°) J; c*’“°”31n'“3d6 98% f1 (1Jt2)g—§€izldt (gy>_%) FPO/+73) 9.6.19 121(2) =1 If 6: “5 3 cos (n8)d9 D (lnrg 2|<ifl _Sin fun g—zcoah I—vtdi O 11' 9.6.21 “’ . “’ cos (3:6) = . = fl_ dt K0612) J; cos (’1' smh t)dt J; «ta—H (33>0) 9.6.22 K,(:6)=scc {-3396} j: cos (a: sinh t) cosh (pad: on =csc Gram) f sin (a: sinh t) sinh (90636 0 (l9?P|<1.$>0) 9.6.23 _fii(%z)r m —zcool1£ ' 29 K,(z)—T(v+%) 0 e slnh tdt 114(92)" m -u _ = 63—- " Hit r6466) . ‘3 ‘ 1) 06 (990—6. Iarg 2I<6n 9.6.24 K.(z)=f c"°°‘*“‘cosh(yt)dt (1.63966) 0 9.6.25 H 119+ %) (26)” °° cos (may?! [C(xa)“ Trim). 0 (t‘z+g2)v+§ (9692—6. 00.196 2K6) Recurrence Relations 9.6.26 fZ"._.(z)—2".+1(z)=%§f’.(5) fl”:(z)=fl”._.(2)~§ 523(2) g.-.(z)+n’.+1(2)=2£;(z) 999:2”... (2) +3 22(2) EX, denotes L, emK. 01' any linear combination of those functions, the coefficients in which are incicpcndcnt of z and v. 9.6.27 13(2)=I1(2), K3(2):—K1(z) Fornullas for Derivatives 9.6.28 (1 i kiz'fé’y(z)}=z”'*§._x(z) :2: dz 1 k (E {245236)} =3—”_kfv-i~k(3) (9:0’1’2’ ‘ ' ') 9.6.29 f;“(::) =% {.“2”._i(z)+(ic)gv—k+2(5) gwfigzw . . . +fl’.+6(z)} (6:033, . . .) Analytic Continuation 9.6.30 L(26“")=6”‘”‘L(z) (m an integer) 9.6.31 K.(ze"“")=e"m”‘K.(2)—1ri sin (mmr) csc (wr)I.(2) (m an integer) 9.6.32 ME) =I.(z), K.(§) =K..(z) (6 real) Generating Function and Associated Series 9.6.33 eiz“+””=i (616(2) (63%) ku—m 9.6.34. 6m”: 0(2)J.--2 no) 66662-6) 9.6.35 8: am E=ID(2) +2 g (_)kfn+1(z) sin { (26;+1)9] +2 (—)RI2;:(ZIJ [103(2fufl). 9.6.36 1=Io(€)-2I2(E)+2L(z)__215(Ej+ - ' I 9.6.37 e=zfo(z)-i—2LC2)+2L{2)+213(z)+ _ h I 9.6.33 e"3:_-Io(3)‘—2I1(€)‘i’2f2(3)-—2f3(z) ‘Ji_ I I - 9.6.39 cosh z=Iu(z)+212(2)+2L(z)+2I.(2)+ - - - 9.6.40 sinh 2:211(z)+2f3(2)+2fs(3)+ . . . DHI‘AR'I'MICNT OI? CU‘IL‘] E‘ZHCIC 0 Lulhcr H. I'Inrlgcs, Sflrrvi'ary NATIONAL BUREAU OF E'I‘ANUARDS O A. V. Aalin, nirnrrlor UN I'I‘IZD S'I'A'I‘EH Handbook of Mathematical Functiong With (ll-2113113., and N‘Iathemalical Tables Formulas, Edited by Milton Ahrumowilz and Irene A. Stcgun National Bureau of Standards Applied Mathematics Series a 55 Issued Ju n c, 1964 by l1": Sllpurinlcmieut ol' chunmuts‘ U.S. Covrrntncnl Printing Office, “'ushiugtnn. 1}.C-. 20-1U2 Fm.- nnlc ...
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SKEP Integral - a&amp;quot;; 4.053 = j .ACEMb) +3?) 5646 17...

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