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修正的 Struve 函式


StruveL
L_nu(z)=(1/2z)^(nu+1)sum_(k=0)^(infty)((1/2z)^(2k))/(Gamma(k+3/2)Gamma(k+nu+3/2))
(1)
=(2(1/2z)^nu)/(sqrt(pi)Gamma(nu+1/2))int_0^(pi/2)sinh(zcostheta)sin^(2nu)thetadtheta,
(2)

其中 Gamma(z)伽瑪函式L_nu(z) 與普通的 Struve 函式 H_n(z) 相關,關係如下:

 L_n(z)=-ie^(-npii/2)H_n(iz)
(3)

(Abramowitz 和 Stegun 1972, 第 498 頁)。

Struve 函式 L_nu(z)Wolfram 語言 中被實現為:StruveL[n, z].

StruveLReIm
StruveLContours

上圖顯示了複平面中的 L_0(z)


另請參閱

Anger 函式, Struve 函式, Weber 函式

相關 Wolfram 站點

http://functions.wolfram.com/Bessel-TypeFunctions/StruveL/

使用 探索

參考文獻

Abramowitz, M. "Tables of Integrals of Struve Functions." J. Math. Phys. 29, 49-51, 1950.Abramowitz, M. and Stegun, I. A. (Eds.). "Modified Struve Function L_nu(x)." §12.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 498, 1972.Apelblat, A. "Derivatives and Integrals with Respect to the Order of the Struve Functions H_nu(x) and L_nu(x)." J. Math. Anal. Appl. 137, 17-36, 1999.Cook, R. K. "Some Properties of Struve Functions." J. Washington Acad. Sci. 47, 365-368, 1957.Horton, C. W. "On the Extension of Some Lommel Integrals to Struve Functions with an Application to Acoustic Radiation." J. Math. Phys. 29, 31-37, 1950.Horton, C. W. "A Short Table of Struve Functions and of Some Integrals Involving Bessel and Struve Functions." J. Math. Phys. 29, 56-58, 1950.Mathematical Tables Project. "Table of the Struve Functions L_nu(z) and H_nu(z)." J. Math. Phys. 25, 252-259, 1946.Prudnikov, A. P.; Marichev, O. I.; and Brychkov, Yu. A. "The Struve Functions H_nu(x) and L_nu(x)." §1.4 in Integrals and Series, Vol. 3: More Special Functions. Newark, NJ: Gordon and Breach, pp. 24-27, 1990.

在 中被引用

修正的 Struve 函式

引用為

Weisstein, Eric W. "Modified Struve 函式。" 來自 -- 資源。 https://mathworld.tw/ModifiedStruveFunction.html

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