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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: 508 CONFLUENT HYPERGEOMETRIC F"Cl'I0NS 13.5. Asymptotic Expansions and Limiting Forms For 1s I larw, (a, b fixed) 13.5.1 and 13.5.4 (b--a)s(l--a)s z-s S! O(l4 -9 = [~-b+2a+z-S+0(lzl-1)1 where the R'th and S t h terms are the smallest in the expansions 13.5.1 and 13.5.2. 13.5.11 13.5.12 For large a (b, s fixed) 13.5.13 M(a, b, z)= r (a) e+Z(+bz-az)+- "Jb-1 (d(2b2- 4az) [1+0(13b-al-91 where Izl-lt )-alp and a=& (1-p, 3-+p), O2b--a>l, 13.5.17 M(a, b, z)=r(b) sin (UT) exp [(b-aa)(\$ sinh SB--B+COS~* 0)l [(b-%) cosh e]1-b[r(3b-~) sinh 201-t [ 1 + O(l3b - 4-9 I 13.5.18 U(U, b, z)=exp [(b-aa)(j sinh 28--8+cosh* 0)l [(b-2a) cosh 13]'-~[((3b-a) sinh 201-1 [1-1-0(l~~-al-31 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.