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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 | MEDIUM | LARGE Below is the OCR-scanned text from this page: 11. Integrals of Bessel Functions Ma thema tical Proper ties 11.1. Simple Integrals of Bessel Functions l t N J v ( t ) d t 11.1.1 It@J.(t)dt= r (F) z p r ( 7 ) V+P+l (v+2k+i)r c++k) X f i Jv+zk+, (2) k=O r ( v + k ) (Wb+V+l)>O) 11.1.2 Recurrence Relations 11.1.5 11.1.6 P 1 ( t ) d t = 1 -Jo(Z) 11.1.7 11.1.8 Soi,(t)dt = zZo(4 +s 1 { -Lo(4 21 (2) +Ll (4Z"(d 1 -2, (2) = AI, (2) + Befv*Kv (z) , Y = 0'1 A and B are constants. H,(z) and Lv(z) are Struve functions (see chapter 12). 11.1.9 y (Euler's constant)=.57721 56649 . . . In this and all other integrals of 11.1, z is real and positive although all the results remain valid for extended portions of the complex plane unless stated to the contrary. 11.1.10 Asymptotic Expansions 11.1.11 m 1 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.