Hi, can someone give me a hand with this "little" integral please.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int (\cos{k})^{t-s+1}(b-a\sin^2k)^{s/2}e^{-ik(n-1)}dk[/tex]

where

t is the time, which is discrete

s is between 0 and t

k has domain [-pi, pi]

n is a natural number

a, b are complex constants

actually this integral is the binomial expansion of this other integral

[tex]\int (\cos{k}+\sqrt{b-a\sin^2k})^t\cos k \quad e^{-ik(n-1)}dk[/tex]

there are some other constants, which I omitted. Also, I am omitting the coefficients and summation of the binomial expansion in the first integral.

I'm looking for a closed form, and I tried using asymptotic approximations but it doesn't work because in general to solve it using asymptotic techniques you need to write it in this form:

[tex]f(k)e^{\phi(k,t)}[/tex]

and I can't do that. Maybe there are some other asymptotic techniques that I don't know, maybe you can also give me a hand on this.

Thanks in advance!!!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Very tricky integral

Loading...

Similar Threads - Very tricky integral | Date |
---|---|

Fitting a (Very) Large Random Number To A Formula | Jul 16, 2015 |

Very brief summnation question | Dec 2, 2014 |

Very very short question on second derivative | Oct 18, 2014 |

Very basic question | Dec 15, 2013 |

Very tricky Fourier transform please help! | Jun 6, 2012 |

**Physics Forums - The Fusion of Science and Community**