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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: 230 EXPONENTIAL INTEGRAL AND RELATED FUNCTIONS Derivatives 5.1.26 dE"z)- --- E,-l(z) ( n = 1 , 2 , 3 , . . .) d z 5.1.27 (-l)"(n- l ) ! ( n = 1 , 2 , 3 , . . .) + 2" Definite and Indefinite Integrals (For more extensive tables of integrals see [5.31, [5.61, [5.11], [5.12], [5.13]. For integrals involving En(x) see [5.9].) e-ai 5.1.28 s, b+t dt=eabEl(ub) 5.1.29 1- & dt=e-fabEl(-iub) (u>o, b>O) 5.1.30 g2 efatdt=eabEl(ub) (u>O, b>O) 5.1.31 b d t = h - 5.1.32 I L- e-aite-bi U 5.1.33 lm E:(t)dt=2 In 2 5.1.34 Lw e-aiEn(t)dt= 5.1.35 s,' ear sin bt b dt=?r-arctan a +YEl(-u+ib) 5.1.36 (u>O, b real) 5.1.37 S,' ea'(l-tcos bt) +9El(-u+ib) (u>O, b real) 5.1.38 s,' e-"(ltcos bt) +9E,(a+ib) (a>O, b real) 5.1.39 s,' d t = E 1 ( z ) + h z+y 5.1.40 dt=Ei (.)-In z--y (z>O) 5.1.41 J& 2a i dz=- [ e-aEl(-u--iz) - eaE,(u-iz)] +cons t. 5.1.42 [ e-"El (-a- iz) + eaEl (u- iz) ] sue9 dx=-- 1 2 +cons t. 5.1.43 JUG dx=-- 1 Y(efaEl (- z+ ia)) +cons t. (a>()) 5.1.44 U dz=-9?(efaEl(-z+ia)) +const. (u>O) J U G Relation to Incomplete Gamma Function (see 6.5) 5.1.45 E,,(z)=z*-lr(i--n, Z ) 5.1.46 an(z)=Z-n-lr(n+ 1, Z ) 5.1.47 pn(Z)=Z-n-l[r(n+ 1, - z ) - r ( n + i , z ) ] Relation to Spherical Beasel Functions (see 10.2) - 5 . ~ 4 8 dz)=dzKt(z), 2 B & ) = ~ l t ( z ) 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.