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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: 13 . Confluent Hypergeometric Functions LUCY JOAN SLATER * Con tents Mathematical Properties . . . . . . . . . . . . . . . . . . . 13.1. Definitions of Kummer and Whittaker Functions . . . . . 13.2. Integral Representations . . . . . . . . . . . . . . . 13.3. Connections With Bessel Functions . . . . . . . . . . . . 13.4. Recurrence Relations and Differential Properties . . . . . 13.5. Asymptotic Expansions and Limiting Forms . . . . . . . 13.6. Special Cases . . . . . . . . . . . . . . . . . . . . 13.7. Zeros and Turning Values . . . . . . . . . . . . . . . Numerical Methods . . . . . . . . . . . . . . . . . . . . . . 13.8. Use and Extension of the Tables . . . . . . . . . . . . 13.9. Calculation of Zeros and Turning Points . . . . . . . . . 13.10. Graphing M(a, b. z) . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . Table 13.1. Confluent Hypergeometric Function M(a. b. z) . . . . . Z= .1 (.1) 1 (1)lO. U= - 1 ( . l ) l , b= .1 (.1) 1. 8s Table 13.2. Zeros of M(a. b. z) . . . . . . . . . . . . . . . . . . U= - 1 (.I) - .I. b=.I(.I)I, 7D Page 504 504 505 506 506 508 509 510 511 511 513 513 514 516 535 The tables were calculated by the author on the electronic calculator EDSACI in the Mathematical Laboratory of Cambridge University. by kind permission of its director. Dr . M . V . Wilkes . The table of M(a. b. 2) was recomputed by Alfred E . Beam for uniformity to eight significant figures . 1 University Mathematical Laboratory. Cambridge . (Prepared under contract with the National Bureau of Standards.) 503 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.