3260 



Definite Integrals (simple) 



3260 



Evaluation, continued. 



approximate, method, Gauss's. Ettingshausen, 



A. von. Baumgartner Z. 7 (1830) 429-. 

 , , . Marko/, A. Mth. A. 25 (1885) 



427-. 

 , , , exposition and generalisation. 



Pujet, A. C. E. 84 (1877) 1071-. 

 , by quadratures. Raabe, J. L. [1836] Crelle 



J. 18 (1838) 75-. 

 case. Krantz,H.J. N. Arch. Wisk. 7 (*1881) 



207-. 

 by double integration. Schlamilch, 0. Grunert 



Arch. 4 (1844) 71-. 

 formula. Cauchy, A. L Gergonne A. Mth. 



16 (1825-26) 97-; 17 (1826-27) 84-. 

 , Cauchy's. Glaisher, J. W. L. [1876] 



Camb. Ph. S. P. 3 (1880) 5-. 

 formulae. Lommel, E. Grunert Arch. 37 



(1861) 433-. 

 . Winckler, A. Wien Sb. 52 (1866) (Ab. 2) 



57-. 



. Stieltjes, . Bll. As. 1 (1884) 568-. 

 , value of residues. Deruyts, J. Par. S. 



Mth. Bll. 14 (1886) 151-. 

 in series. Glaisher, J. W. L. B. A. Ep. 42 



(1872) (Sect.) 15-. 

 theorem. Raabe, J. L. Ziir. Mt. 1 (Heft 3) 



(1848-49) 256-. 



Expansion. Grunert, J. A. Crelle J. 8 (1832) 

 146-. 



. Arndt, F. Grunert Arch. 11 (1848) 70-. 



in continued fractions. Stieltjes, T. J. QJ. 

 Mth. 24 (1890) 370-. 



-- series. Worontzoff, . N. A. Mth. 10 



(1891) 158-. 

 First principles developed without the notion 



of differentials. Hoppe, R. Arch. Mth. Ps. 



61 (1877) 270-. 

 Formula of Abel, generalisation of a. Sonine, 



N. Acta Mth. 4 (1884) 171-. 



, Gauss's, remainder in. \y = I F (t) dt, 



T-t 

 t = t l + ^ + &c\ Sabinin, E. T. [1866] 



(xn) Kec. Mth. (Moscou) 2 (1867) (Pt. 1) 



, general. Dawidoff, A. Liouv. J. Mth. 8 

 (1882) 389-. 



, new. Glaisher, J. W. L. Ph. Mg. 48 

 (1874) 53-. ' 



, . O'Kinealy, J. Ph. Mg. 48 (1874) 



of Poisson's for /(- nh) +/(- nh + h) 

 + /( - nh + 2h) + ... + f (nh -h) + %f(nh). 

 Schaar, M. Brux. Mm. Cour. 4, 23 (1848- 

 50)17 pp. 



Liouville, J. Liouv. J. Mth. 20 (1855) 115-. 

 formulae, Bierens de Haan's. Lindman, C. F. 



Stockh. Ofv. (1890) 353-; Fschr. Mth. (1890) 



293. 

 , development. Schldmilch, 0. Grunert 



Arch. 1 (1841) 263-. 



formulae, inverse method. Nieuport, C. F. F. de. 



[1817] Brux. Ac. Sc. Mm. 1 (1820) 3-. 

 and methods. Winckler, A. Wien Sb. 60 



(1870) (Ab. 2) 857-. 



Fourier-Bessel function - I e ixeata da. Lerch, 



M. Mb. Mth. Ps. 1 (1890) 105-. 

 Fourier's integrals, and analogues. Frombeck, 



H. Wien Sb. 65 (1872) (Ab. 2) 133-. 

 Fresnel's integrals. Jamet, V. N. A. Mth. 15 



(1896) 372-. 

 . Godefroy, . N. A. Mth. 17 (1898) 



205-. 

 Frullani's formula, extension. Lerch, M. 



[1891] Prag Cesk6 Ak. Fr. Jos. Ez. (Tfida 2) 



1 (1892) Art. 8, 1-. 

 Function under definite integral, to find. 



Liouville, J. Par. EC. Pol. J. 24 cah. (1835) 



55. 



r~2 

 Functions, cotan. integral, H (a) = I xcotaxdx. 



Lindman, C. F. Ups. N. Acta S. Sc. 1 (1854) 

 137-. 



differing very little from zero. Cebysev, P. 

 [1873-80] St Pet. Ac. Sc. Mm. (Rs.) 22 

 (*1873) (Suppl.) No. 1, 32 pp. ; 40 (*1882) 

 (Suppl.)No. 3, 



Hermite's integral / x 2 (au + bv)~ z dx. Sincov, 



D. Kazan S. Ps.-Mth. Bll. 4 (1895) (Prot.) 



76-; Fschr. Mth. (1895) 314. 

 Historical note. Escher, R.J. N. Arch. Wisk. 



18 (1891) 142-. 

 Inequalities. Sonin, N. Ja. St Pe"t. Ac. Sc. 



Mm. 6 (1898) No. 6, 54 pp. ; Fschr. Mth. 



(1898) 254. 



of Cebysev, proof. Markoff, A. Mth. A. 24 

 (1884) 172-. 



Integral residues giving approximate values of 

 definite integrals. CebySev, P. [1886] St 

 Pet. Ac. Sc. Mm. (Rs.) 55 (1887) (Suppl.) 

 No. 2, 50 pp.; Acta Mth. 12 (1889) 287-. 



sine and integral cosine. Schldmilch, 0. 

 Grunert Arch. 11 (1848) 389-; Schlomilch 

 Z. 5 (1860) 294-. 



. Besso,D. G. Mt. 6 (1868) 313-. 



related definite integrals. Stefan, J. 



Wien Jbr. Ober-Eealsch. Inn. Stadt 4 (1862) 



Integrals involving cubic radicals, identity. 



Thomae, C. J. Gott. Nr. (1877) 223-. 

 , numerical values, accuracy. Sonin, N. Ja. 



St Pet. Ac. Sc. Mm. (Rs.) 69 (1892) 1- ; 



Fschr. Mth. (1892) 272-. 

 Integration under finite forms. Genocchi, A. 



[1864-72] Tor. Mm. Ac. Sc. 23 (1866) 299- ; 



28 (1876) 1-. 



formula of Jacobi. Kronecker, L. Berl. 

 Ak. Sb. (1884) 539-. 



by means of selected values of function. 

 Woolhoutse, W. S. B. I. Act. J. 27 (1889) 122-. 



of simplest integrals containing cube-roots. 

 Sonin, N. St Pet. Ac. Sc. Bll. 12 (1900) 411- ; 

 Fschr. Mth. (1900) 308. 



278 



