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  • Sum of series:
  • x^n/n
  • 1/n^6 1/n^6
  • 1/n^n 1/n^n
  • (n-1)/n! (n-1)/n!

  • Identical expressions

  • t^k*(- one)^k*a^(two *k)*cos(a*x)*e^(a*z)/factorial(k)
  • t to the power of k multiply by ( minus 1) to the power of k multiply by a to the power of (2 multiply by k) multiply by co sinus of e of (a multiply by x) multiply by e to the power of (a multiply by z) divide by factorial(k)
  • t to the power of k multiply by ( minus one) to the power of k multiply by a to the power of (two multiply by k) multiply by co sinus of e of (a multiply by x) multiply by e to the power of (a multiply by z) divide by factorial(k)
  • tk*(-1)k*a(2*k)*cos(a*x)*e(a*z)/factorial(k)
  • tk*-1k*a2*k*cosa*x*ea*z/factorialk
  • t^k(-1)^ka^(2k)cos(ax)e^(az)/factorial(k)
  • tk(-1)ka(2k)cos(ax)e(az)/factorial(k)
  • tk-1ka2kcosaxeaz/factorialk
  • t^k-1^ka^2kcosaxe^az/factorialk
  • t^k*(-1)^k*a^(2*k)*cos(a*x)*e^(a*z) divide by factorial(k)

  • Similar expressions

  • t^k*(1)^k*a^(2*k)*cos(a*x)*e^(a*z)/factorial(k)
Sum of series/ t^k*(-1)^k*a^(2*k)*cos(a*x)*e^(a*z)/factorial(k)

Sum of series t^k*(-1)^k*a^(2*k)*cos(a*x)*e^(a*z)/factorial(k)


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The solution

You have entered [src] 
  oo                             
____                             
\   `                            
 \     k     k  2*k           a*z
  \   t *(-1) *a   *cos(a*x)*E   
  /   ---------------------------
 /                 k!            
/___,                            
k = 0
$$\sum_{k=0}^{\infty} \frac{e^{a z} a^{2 k} \left(-1\right)^{k} t^{k} \cos{\left(a x \right)}}{k!}$$ 
Sum(((((t^k*(-1)^k)*a^(2*k))*cos(a*x))*E^(a*z))/factorial(k), (k, 0, oo))
The answer [src] 
                   2
          a*z  -t*a 
cos(a*x)*e   *e
$$e^{a z} e^{- a^{2} t} \cos{\left(a x \right)}$$ 
cos(a*x)*exp(a*z)*exp(-t*a^2)

    Examples of finding the sum of a series

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