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143 E. 153426 = ;(l _ =pj O,sg6%5! 1 39 16 36 w- 252 F. 338 B, I 53Li2b ‘-@q-7 H. 0, osq3@574P 50 476 C. 370 * 46 SUMMATION OF SERI&S Series No. 5 + -2e4e6a8 +... 6 O” +“* (254) 1 - 12 + F4 - E + . . 371 A. 190 n+l F. - 2n+1 + (- ‘)“+I > F. 6.. (2n + 2) F. 333 =-- 3 4 W~~~5u3wio T. 144 0,\7%Z4 (367&&j@ T. 144 ~~612s4ql5~ T. 144 logh 2 --1 ‘IT -l”gh3) 43 ( +z ’ logh 2 =4 =$(l+&-; = ; logh 2 = 1/2 0, logh 3 ~J@+f3~635cf P-i0 o, \73’S%7 qst T. 144 c. 252 48 SUMMATION OF SERIES Series No. 9 4 +-*.

243 . = i tan-l x + i logh (1 + x2) . 80 30 SUMMATION OF SERIES Series No. x2 x4 (157) ; - z;i + m. -. . 00 (158) x + ; + ; + $ - 7 + f + . . 00 (159) Reversion of Series. Y = x - blX2 - bgc3 - bp? -. . ccl cm become x = Y + GY2 + c2y3 + c3y4 + . . 09 if Cl c2 c3 c4 c5 c6 c7 See Van Orstrand (Phil. Msg. 1910) for coefficients up to C,,. 3(n1+ 1)2 - 3$+ (161) 1 + ; + ; + $ + . . co . . (162) $ + & + k6 + . . co (163) ; + $2 + k3 + . . 00 1)3 -“- O” EXPONENTIAL AND LOGARITHMIC SERIES 31 Reference = logh 3 Y.

20 (127) f logh n + logh (n + 1) + . . m (128) 2 [n logh (2#) - l] I (129)x++~x~+... (130) 1 + (x0) co + $ (XC-y + $(XP)’ + $(xc-)4 + . . co = 1+2 cn“,t’“-’(xe-x)” I x3 x5 x7 (131) m + c5 + c7 +. . 00 (if convergent) (132)t 1 - 2(2 - lp, ; + 2(23 - 1)~~ $ - 2(25 - l)B,g X6 +. . co (133)t1+2ux+(2C7)+2(~+x)+;B,}+yB2(;+x) +qgE4(k+x) t For values of B,,(x), see No. (1146). 4B2}+... f - n logh : where m and n integers = ; (1 - logh 2) logh {x + 2/l + x2} where 1x1 Q 1 = ,p x. 141 x. 141 A. 526 A.

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