隆梅爾函數是下列隆梅爾方程的兩類解:
![Thumb](http://upload.wikimedia.org/wikipedia/commons/thumb/3/36/LommelS1.png/320px-LommelS1.png)
![Thumb](http://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/LommelS2.png/320px-LommelS2.png)
1880年數學家隆梅爾首先給出隆梅爾方程的兩個解,稱為隆梅爾函數:
其中 Jν(z) 是第一類貝索函數, Yν(z) 是第二類貝索函數。
參考文獻
- Erdélyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G., Higher transcendental functions. Vol II (PDF), McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953 [2014-05-31], MR 0058756, (原始內容存檔 (PDF)於2011-07-14)
- Lommel, E., Ueber eine mit den Bessel'schen Functionen verwandte Function, Math. Ann., 1875, 9 (3): 425–444, doi:10.1007/BF01443342
- Lommel, E., Zur Theorie der Bessel'schen Funktionen IV, Math. Ann., 1880, 16 (2): 183–208, doi:10.1007/BF01446386
- Paris, R. B., 隆梅尔函数, Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (編), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248
- Solomentsev, E.D., l/l060800, Hazewinkel, Michiel (編), 数学百科全书, Springer, 2001, ISBN 978-1-55608-010-4
外部連結
- Weisstein, Eric W. "Lommel Differential Equation." (頁面存檔備份,存於互聯網檔案館) From MathWorld—A Wolfram Web Resource.
- Weisstein, Eric W. "Lommel Function." (頁面存檔備份,存於互聯網檔案館) From MathWorld—A Wolfram Web Resource.
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