phi是无理数

Any Questions?

http://url.cn/KtHU0C

(摘自Computer-Assisted Discovery and Proof (David H. Bailey Jonathan M. Borwein) (摘自Harmonic sums Mellin transforms and Integrals,J. A. M. Vermaseren NIKHEF)

利用傅里叶正弦变换，可以方便地求出右方的积分 或者写作 对参数a在零点处展开，容易得到Eisenstein型级数的和

http://url.cn/IAnhqc http://url.cn/EqPw89 计划今年证明完这两个，最近太忙，先放上部分

我记得当年高中数学老师教给我们任意整数有限的数列都能写出一个通项公式的方法，但我忘了，现在请问各位这个方法？或者1,3,5,7,100这个数列的通项公式能帮我写一下吗？

1.Integrals of the Ising class (D.H. Bailey J.M. Borwein R.E.Crandall) 2.Hypergeometric forms for Ising-class integrals (D.H. Bailey, D. Borwein, J.M. Borwein,R.E. Crandall) 3. Finding General Explicit Formulas for Ising Integral Recursions (D.H. Bailey J.M. Borwein) 4.On Recurrences for Ising Integrals (Johannes Kepler University Linz, Austria)

http://url.cn/JntP5j

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=151&amp

其中Hk是调和函数

！寒假研究

求教一题@creasson

已知凸五边形ABCDE， 三角形ABE的面积为a， 三角形BCA的面积为b， 三角形CDB的面积为c， 三角形DEC的面积为d， 三角形EAD的面积为e， 五边形ABCDE的面积为s， 求证：s²-（a+b+c+d+e）s+ab+bc+cd+de+ea=0

最后一式可用来求数值结果，500位小数：0.5665817389096680905241983285626712106470690998824521894093798115158281491546436550234864873756500964369970681674446108223470168228796109947696377663441479303799010536388344472384851166034238733470267223824932851967509977876618107531732711263586011761711183819561210960212659003714333318673306348109846604739226129476167930999757570240713511991173384896967970901252642685906499798558015471196272536211400490994969100447394199118081286001227185186022487026395135570686768343659452381802016915406918524719

感觉是用留数，但不知道用什么路径去做 @creasson 大神给个可用的路径吧，剩下的我自己做做

1.THREE TRIPLE INTEGRALS (G. N. WATSON) 2.WATSON'S THIRD INTEGRAL (Hannah Cairns) 3.ON THE EVALUATION OF GENERALIZED WATSON INTEGRALS (G. S. JOYCE AND I. J. ZUCKER)

1.Euler Sums and Contour Integral Representations (Philippe Flajolet and Bruno Salvy) 2.Experimental evaluation of Euler sums (D.H.Bailey J.M.Borwein andR.Girgensohn) 3.Evaluation of triple euler sums (Jonathan M. Borwein) 4.Harmonic sums,Mellin transforms and Integrals (J.A.M.Vermaseren,NIKHEF)

1.Box integrals (D.H. Bailey J.M. Borwein R.E. Crandall) 2.Higher-dimensional box integrals (Jonathan M. Borwein O-Yeat Chan y R. E. Crandall) 3.ADVANCES IN THE THEORY OF BOX INTEGRALS (D. H. BAILEY, J. M. BORWEIN, AND R. E. CRANDALL)

1.Ising Integrals 2.watson Integrals 3.Box Integrals 4.spin integrals 5.Lattice Sum 6.Euler Sum 7.Meijer G function 8.Ramanujan-type series 9.PSLQ