3250 



Integrals 



3250 



Integrals, remarkable. Pomey, E. N. A. Mth. 

 7 (1888) 191-. 



and sums, value. Popov, A. T. (xn) Kazan 

 Un. Mm. (1851, Bk. 4) 1-. 



, transformation. Bouniakowsky, V. St 



P6t. Ac. Sc. Bll. 2 (1860) 136-. 

 , . CebySev, P. [1883] St Pet. Ac. Sc. 



Mm. (Rs.) 47 (1884) (Suppl.) No. 4, 17 pp. 

 , , formulae. Schlomilch, 0. Grunert Arch. 



10 (1847) 440-. 

 , , method depending on square roots, 



application to geodesy. Callandreau, 0. C. 



E. 85 (1877) 664-, 1062-. 

 , of sums. Cauchy, A. L. C. E. 13 



(1841) 181-. 

 , transformations. Bronwin, B. Camb. Mth. 



J. 2 (1841) 263-; 4 (1845) 233-; Mathe- 

 matician 3 (1850) 135-. 



, value. Stern, M. A. Crelle J. Mth. 78 

 340- ; 79 (1875) 263-. 



. , theory. Plana, G. Gergonne A. 

 log a;' 



Mth. 12 (1821-22) 145-. 



, (Plana). Anon, (vi 544) Gergonne 



A. Mth. 12 (1821-22) 365-. 



I . Verdam, G. J. Grunert Arch. 4 



(1844) 221-. 

 . Schlomilch, 0. Grunert Arch. 6 (1845) 



326-. 

 . Young, J. R. Ph. Mg. 32 (1848) 



lx~ l dx, symbolical value. Center, W. 



Camb. and Dubl. Mth. J. 4 (1849) 261-. 

 x\b 

 j4- , fractional integration. Oettinger, 



L. Grunert Arch. 15 (1850) 424-. 



^x + 2 N/o 7 . Schulze, N. W. Grunert Arch. 

 19 (1852) 181-. 



(Schulze). Lindman, C. F. Grunert 

 Arch. 23 (1854) 445-. 



/ d<f> sin 2 "0 (1 - k sin 2 <)", solution. Schon- 

 bichler, K. Wien SB. 16 (1855) 447-. 



'-y A~I~. Grunert, J. A. Grunert 



[ 



I 

 J 



Arch. 27 (1856) 362-. 



, evaluation. Gauss, C. F. 



*Ja + bx -f ex 2 

 Grunert Arch. 30 (1858) 229-. 



l\/a*-x 2 dx in connection with other in- 

 tegrals. Fischer, . Grunert Arch. 38 

 (1862) 151-. 

 dx 



~/(^ 



Spitzer, S. Grunert 



Arch. 40 (1863) 168-. 



[ x m dx 

 I , a . Hermite, C. A, Mt. 1 (1867-68) 



155-. 



am 



i 



187 



Integrals I e" in x cos (nx - cos x) dx, &c. Unfer- 

 dinger, F. Wien Sb. 57 (1868) (Ab. 2) 611-. 



I x n . cos {wtlg (a + bx) } dx, &c. Unferdinger, 



Wien Sb. 59 (1869) (Ab. 2) 437-. 

 \ CO s?m+i x dx. Realis, S. N. A. Mth. 13 

 (1874) 83-. 



I tj>(x \dx=.\ <j>(x)dx, proof. 



Glaisher, J. W. L. Mess. Mth. 4 (1875) 

 186-. 



I (u) n du, infinite values. Schroder, E. Z. 



Mth. Ps. 25 (1880) 106-. 



, (Schroder). Schlomilch, 0. X. Z. 



Mth. Ps. 25 (1880) 117-. 



I f(z) dz over a surface containing no singu- 

 larity of/ (z). Rados, I. [1884] Mth. Termt. 

 Ets. 3 (1885) 46-; Mth. Nt. B. Ung. 3 (1884- 

 85) 186-. 



lf(x)cosxdx, and the equation -^ 



+ y=f(x). Studntika, F. J. Casopis 13 



(1884) 12-; Fschr. Mth. (1884) 235. 



I e" x f (x) dx. Gomes-Teixeira, F. Em. E. 

 Ac. Line. Ed. 1 (1885) 278-. 



e z<l I e~ zZ dz, semi-convergent series for. 



J z 



Schols, C. M. Delft EC. Pol. A. 1 (1885) 

 213- ; Amst. Ak. Vs. M. 2 (1886) 40-. 



I -j=. where X is reciprocal cubic or quartic. 

 J vX 



Toropov, K. A. Kharkov Mth. S. Com. 



(1885) 3-; Fschr. Mth. (1885) 258. 



Ml +z 2 )-" dz. Balitrand, . N. A. Mth. 



6 (1887) 45-. 



f sin z , , f cos z , 



I dz and | dz. Linhardt, E. 



J z a J z a 



Arch. Mth. Ps. 5 (1887) 91-. 



Idxl^+paf + q. Dolbnia, J. Bll. So. 

 Mth. 19 (1895) 76-. 



I logsecxdx, proposed tabulation. Mc- 



Mahon, J. Science 4 (1896) 345. 



_i_ 



,-| m 



) . Iwanow, 



T. J. Fschr. Mth. (1899) 271. 

 Integrating equation. Jong, J. de. Arch. N6erl. 

 7 (1872) 140-. 



INTEGEATION. 



Le Barbier, Gergonne A. Mth. 20 (1829- 

 30) 117- ; 21 (1830-31) 73-. 



270 



