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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: 7. Error Function and Fresnel Integrals WALTER GAUTSCHI Contents Page Mathematical Properties . . . . . . . . . . . . . . . . . . . . 297 7.1. Error Function . . . . . . . , . . . . . . . . . . . . . . 297 7.2. Repeated Integrals of the Error Function . . . . . . . . . . 299 7.3. Fresnel Integrals . . . . . . . . . . . . . . . . . . . . . 300 7.4. Definite and Indefinite Integrals . . . . . . . . . . . . . . 302 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . 304 7.5. Use and Extension of the Tables . . . . . . . . . . . . . . 304 References . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Table 7.1. Error Function and its Derivative ( 0 5 x 5 2 ) . . . . . . 310 (2/&)e-z2, erf x=(2/&) Jz e-c2dt, x=0(.01)2, 10D 0 Table 7.2. Derivative of the Error Function ( 2 5 x 5 1 0 ) . . . . . . 312 (2/J;;)e-z2, x=2(.01)10, 8s Table 7.3. Complementary Error Function ( 2 5 x 5 a). . . . . . . 316 xex2 erfc x= (2/J;;)xez2 e-12dt, ~-~=.25(-.005)0, 7D erfcfi, n=1(1)10, 15D r Table 7.4. Repeated Integrals of the Error Function (05x<5) . . . 317 ~=0(.1)5,n=1(1)6, 10, 11, 6 s Table 7.5. Dawson’s Integral ( 0 5 x 5 w ) . . . . . . .. . . . . . . 319 e-z21ec2dt, x=0(.02) 2, 10D xe-221ez2dt, ~-~=.25(-.005)0, 9D 1 Guest worker, National Bureau of Standards, from The American University. (Presently Purdue University .) 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.