共查询到20条相似文献,搜索用时 421 毫秒
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对含参数反常积分I(t,s)=∫+∞0 x-1(1+x)-sdx,由贝塔函数的积分表示得到I(t,s)的伽马函数表示,再由伽马函数的级数展开,得到I(t,s)的参数级数展开.I(t,s)可在积分符号内按参数展开,参数系数是含对数函数的反常积分.对比同类参数的系数,可得一系列含对数函数反常积分的值. 相似文献
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定义了三种积分表示的两元函数.这些两元函数有伽马函数表示,可以展开为幂级数.在积分符号内展开被积函数,先积分,再求和,也得到级数展开.对比展开系数,就得到一些对数三角函数定积分的值.选取合适的围道,得到其他两类对数三角函数定积分的值. 相似文献
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重点讨论了索赔次数服从于二项分布的情况下单个险种和多个险种的聚合风险模型,得出了在此情况下求其分布函数的若干方法,并给出聚合理赔量的两种近似模型,正态近似和平移伽马近似.最后给出了一个数值例子,验证了本文的分布函数的若干求法. 相似文献
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《数学的实践与认识》2015,(24)
将泊松分布参数的充分统计量的离散型分布函数转化为生存伽马分布函数,以此为枢轴量构造了泊松分布参数的精确置信区间.通过数值模拟,选择合适的置信度组合,得到精确最短置信区间.讨论了大样本下泊松分布参数的近似置信区间的估计精度,验证了精确最短置信区间的计算结果. 相似文献
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关于伽马分布及相关分布性质的一点研究 总被引:1,自引:0,他引:1
主要研究伽马分布的性质,并通过对伽马分布可加性的研究.得到由指数分布通过伽马分布构造卡方分布和均匀分布的方法,通过本文可以加深对伽马分布和其它常见连续性分布关系的认识. 相似文献
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We present a Fourier transform representation of the generalized gamma functions, which leads to a distributional representation for them as a series of Dirac-delta functions. Applications of these representations are shown in evaluation of the integrals of products of the generalized gamma function with other functions. The results for Euler’s gamma function are deduced as special cases. The relation of the generalized gamma function with the Macdonald function is exploited to deduce new identities for it. 相似文献
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Edward Neuman 《Results in Mathematics》2013,63(3-4):1209-1214
Inequalities involving the incomplete gamma function are established. They are obtained using logarithmic convexity of some function associated with the function in question. Lower and upper bounds for the incomplete gamma function are also derived. Bounds for the error function erf are also established. 相似文献
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We unify several asymptotic expansions for the gamma function due to Laplace, Ramanujan–Karatsuba, Gosper, Mortici, Nemes and Batir. Furthermore we present new asymptotic expansions for the gamma function. 相似文献
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Atsushi Narukawa 《Advances in Mathematics》2004,189(2):247-267
We show the modular properties of the multiple “elliptic” gamma functions, which are an extension of those of the theta function and the elliptic gamma function. The modular property of the theta function is known as Jacobi's transformation, and that of the elliptic gamma function was provided by Felder and Varchenko. In this paper, we deal with the multiple sine functions, since the modular properties of the multiple elliptic gamma functions result from the equivalence between two ways to represent the multiple sine functions as infinite products.We also derive integral representations of the multiple sine functions and the multiple elliptic gamma functions. We introduce correspondences between the multiple elliptic gamma functions and the multiple sine functions. 相似文献
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In this paper we prove new complete monotonicity properties of some functions involving the gamma function. As consequences of them we establish various new upper and lower bounds for the gamma function and the harmonic numbers. 相似文献
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Yaming Yu 《Expositiones Mathematicae》2009,27(2):171-174
We prove a class of double inequalities for the gamma function which were conjectured by Batir [On some properties of the gamma function, Expo. Math. 26 (2008) 187–196]. 相似文献
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杨明顺 《数学的实践与认识》2009,39(10)
由Riemannζ函数的函数方程得到Hurwitzζ函数的Hermite公式,再从Hermite公式得到Γ(s)的Binet′s第二表达式,从而由ζ函数推得Γ(s)的性质. 相似文献
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Mitsuhiko Kohno 《Journal of Difference Equations and Applications》2013,19(5):701-716
To the author's knowledge, among the so—called special functions, the gamma function is a unique one which is defined by a linear difference equation and is a hyper—transcendental function. There exists an another well—known hyper—transcendental function called the psi function, which is merely the logarithmic derivative of the gamma function. In this paper the author consider an extension of the gamma function and then obtain a series of integrals of the psi function. 相似文献
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Chao-Ping Chen 《Numerical Algorithms》2013,64(2):311-319
We consider a class of the asymptotic expansions for the gamma function, and derive a formula for determining the coefficients of the asymptotic expansions. Thus, we give a unified treatment of several asymptotic expansions for the gamma function due to Laplace, Ramanujan–Karatsuba, Gosper, Mortici and Batir. 相似文献
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J. M. B. Noronha 《Integral Transforms and Special Functions》2017,28(6):423-442
We provide new representations for the finite parts at the poles and the derivative at zero of the Barnes zeta function in any dimension in the general case. These representations are in the forms of series and limits. We also give an integral representation for the finite parts at the poles. Similar results are derived for an associated function, which we term homogeneous Barnes zeta function. Our expressions immediately yield analogous representations for the logarithm of the Barnes gamma function, including the particular case also known as multiple gamma function. 相似文献