百科问答小站 logo
百科问答小站 font logo



请问这个如何做? 第1页

  

user avatar   ysw-13 网友的相关建议: 
      

The final result converges to the Gelfond constant .This is not an ordinary question.This sequence is mentioned in the book Mathematics by Experiment: Plausible Reasoning in the 21st Century.

The solution of Paramanand Singh is given below.


Let be the elliptic modulusand then we define complementary modulus .Further the complete elliptic integrals of the first kind are defined by

By the way the use of prime here does not denote derivative.

Starting with a modulus we define a new modulus via ascending Landen transformation

where is complementary to ie . It can be proved with some effort that

Using a little amount of algebra it can be seen that the relation between and is same as the relation between and and hence from the above equation we get

and therefore from the last two equations we get

Corresponding to elliptic modulus we have another variable called nome defined by

and it is possible to get an expression for in terms of via the use of theta functions. We have

where

The sequence in question is descending Landen sequence of elliptic moduli and using equation we have

The corresponding nomes have a relation between them as Thus we can see that

Next also note that as and using we have the relation

The desired relation follows easily from and and the relation




  

相关话题

  综合除法的数学依据是什么? 
  [-5e^(2i*π)+1*3]/2=1*4这一串有什么特殊意义吗? 
  如何证明欧拉函数是积性函数? 
  有没有可能把 π 或 e 等无理数当成 1,这样就能使许多定理显而易见? 
  研究数学花钱多吗? 
  为什么∫x²/(√1-x²)dx用分部积分求不出来不定积分? 
  如下,命题是否正确,如果正确,又是如何得出的? 
  如何成为一名科研人员(最好是数学)? 
  狼想吃掉羊,狮子要保护羊,他能做到吗? 
  a,b,c,d 是正实数,且 a²+b²+c²+d²+abcd=5,怎么证明 a+b+c+d≤4? 

前一个讨论
怎样评价《逃避可耻但有用》?
下一个讨论
数学知识能否无中生有?





© 2025-06-28 - tinynew.org. All Rights Reserved.
© 2025-06-28 - tinynew.org. 保留所有权利