Equazione ipergeometrica confluente: differenze tra le versioni
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Riga 12:
La funzione ipergeometrica di Kummer è data dalla [[serie ipergeometrica generalizzata]]:
:<math>M(a,b,z)= 1 + \frac{a}{b}z + \frac{a(a+1)}{b(b+1)}\frac{z^2}{2!} + \dots =\sum_{n=0}^\infty \frac {(a)_n\, z^n} {(b)_n\,n!} = {}_1F_1(a;b;z)</math>
dove:
Riga 33:
* {{en}}Arthur Erdélyi,Whilhelm Magnus, Fritz Oberhettinger, Francesco Tricomi (1953) ''Higher transcendental functions'' Vol. I, Krieger Publishing, Ristampa Mc Graw-Hill (1981), Chapter VI.
* {{en}}A. D. MacDonald ''[http://hdl.handle.net/1721.1/4966 Properties of the Confluent Hypergeometric Function]'' (RLE Technical Report, MIT, 1948)
* {{fr}}
* {{en}}Milton Abramowitz, Irene A. Stegun (1964): ''Handbook of Mathematical Functions'', Dover Publications, New York. ISBN 0-486-61272-4, [http://www.math.sfu.ca/~cbm/aands/page_503.htm Capitolo 13].
* {{en}}Arfken, G. "Confluent Hypergeometric Functions." §13.6 in ''Mathematical Methods for Physicists, 3rd ed''. Orlando, FL: Academic Press, pp. 753-758, 1985.
* {{en}}Morse, P. M. and Feshbach, H. ''Methods of Theoretical Physics'', Part I. New York: McGraw-Hill, pp. 551-555, 1953.
* {{en}}Slater, L. J. ''Confluent Hypergeometric Functions''. Cambridge, England: Cambridge University Press, 1960.
* {{en}}Zwillinger, D. ''Handbook of Differential Equations'', 3rd ed. Boston, MA: Academic Press, pp. 123-124, 1997.
== Voci correlate ==
Line 47 ⟶ 51:
*{{mathworld|ConfluentHypergeometricFunctionoftheFirstKind|Confluent Hypergeometric Function of the First Kind}}
*{{mathworld|ConfluentHypergeometricFunctionoftheSecondKind|Confluent Hypergeometric Function of the Second Kind}}
* {{en}}[http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric1F1/ Kummer hypergeometric function] su Wolfram Functions site
* {{en}}[http://functions.wolfram.com/HypergeometricFunctions/HypergeometricU/ Tricomi hypergeometric function] su Wolfram Functions site
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