The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" ...The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.展开更多
目的探讨血清γ-谷氨酰基转移酶(GGT)、丙氨酸氨基转移酶(ALT)对2型糖尿病早期诊断的临床应用价值。方法采用Roche Modu lar全自动生化分析仪及配套试剂检测200例2型糖尿病患者(男、女各100例)及200名正常对照者的血清葡萄糖(G lu)、GGT...目的探讨血清γ-谷氨酰基转移酶(GGT)、丙氨酸氨基转移酶(ALT)对2型糖尿病早期诊断的临床应用价值。方法采用Roche Modu lar全自动生化分析仪及配套试剂检测200例2型糖尿病患者(男、女各100例)及200名正常对照者的血清葡萄糖(G lu)、GGT和ALT水平,并进行统计分析。结果 2型糖尿病患者男性及女性的G lu、GGT水平与对照组比较,差异均有统计学意义(P<0.05),而ALT则无差异;男性和女性2型糖尿病患者中GGT浓度超出参考区间的百分率分别是13%和16%,明显高于对照组。结论 GGT对于2型糖尿病的早期诊断有一定意义。展开更多
文摘The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.
