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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: 498 STRUVE FUNCTIONS AND RELATED FUNCTIONS Asymptotic Expansions for Large Orders 12.1.34 12.2. Modified Struve Function L,(z) Power Series Expansion f Y T 12.2.1 L,(z)=-ie-TEv(iz) Integral Representations * @v>--3i) 12.2.3 Recurrence Relations W X , /’ - I - , FIGURE 12.4. Modijied Struve junctions. L.(z), fn=0(1)5 .See page n. Asymptotic Expansion for Large I z I 12.2.6 LY(~)-I-,(~) Integrals 12.2.7 2 (2k)! (2k-l)! +-- A k - 1 2 (k!)2(22)* (larg ZI<\$A) 2 12.2.9 I’ L1(t)dt=L0(z)-- z A Relation to Modified Sphericti1 Bessel Function 12.2.10 L-(,,++l (z)=I(,++)(z) (n an integer2O) 12.3. Anger and Weber Functions Anger’s Function 12.3.1 J,(z) =: 1 cos ( Y e - z sin 0) de 12.3.2 J,(z)=J,(z) (n an integer) Weber’s Function 12.3.3 EY(z) =A s‘ sin (YO- z sin e) do A 0 Relations Between Anger’s and Weber’s Function 12.3.4 sin (m) J,(z)=cos (m) E,(z)-E-,(z) 12.3.5 sin (m) E,(z)=J-”(2)-cos (m) J,(z) Relations Between Weber’s Function and Struve’s Function If n is a positive integer or zero, rn-ii 12.3.7 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.