Integral de sinc(x)*cos(ax) dx

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|pi*|<                 a                    for |a | < 1|                                  
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|   ||\_|2, 2 \ 0   -1/2 | polar_lift (a)/              |                                  
<   \\                                                  /         /                1      \
|--------------------------------------------------------  for And|2*|arg(a)| = 0, -- != 1|
|                           a                                     |                 2     |
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|                 oo                                                                       
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|                 |  cos(a*x)*sinc(x) dx                              otherwise            
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|                /                                                                         
|                -oo                                                                       
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$$\begin{cases} \frac{\pi \left(\begin{cases} 0 & \text{for}\: \frac{1}{\left|{a^{2}}\right|} < 1 \\a & \text{for}\: \left|{a^{2}}\right| < 1 \\{G_{2, 2}^{1, 1}\left(\begin{matrix} \frac{1}{2} & 0 \\0 & - \frac{1}{2} \end{matrix} \middle| {\frac{1}{\operatorname{polar\_lift}^{2}{\left(a \right)}}} \right)} & \text{otherwise} \end{cases}\right)}{a} & \text{for}\: 2 \left|{\arg{\left(a \right)}}\right| = 0 \wedge \frac{1}{a^{2}} \neq 1 \\\int\limits_{-\infty}^{\infty} \cos{\left(a x \right)} \operatorname{sinc}{\left(x \right)}\, dx & \text{otherwise} \end{cases}$$

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/   //                                           1      \                                  
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|   ||                                          |a |    |                                  
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|pi*|<                 a                    for |a | < 1|                                  
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|   ||        /          |       1       \              |                                  
|   || __1, 1 |1/2   0   | --------------|              |                                  
|   ||/__     |          |           2   |   otherwise  |                                  
|   ||\_|2, 2 \ 0   -1/2 | polar_lift (a)/              |                                  
<   \\                                                  /         /                1      \
|--------------------------------------------------------  for And|2*|arg(a)| = 0, -- != 1|
|                           a                                     |                 2     |
|                                                                 \                a      /
|                                                                                          
|                 oo                                                                       
|                  /                                                                       
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|                 |  cos(a*x)*sinc(x) dx                              otherwise            
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|                /                                                                         
|                -oo                                                                       
\                                                                                          

$$\begin{cases} \frac{\pi \left(\begin{cases} 0 & \text{for}\: \frac{1}{\left|{a^{2}}\right|} < 1 \\a & \text{for}\: \left|{a^{2}}\right| < 1 \\{G_{2, 2}^{1, 1}\left(\begin{matrix} \frac{1}{2} & 0 \\0 & - \frac{1}{2} \end{matrix} \middle| {\frac{1}{\operatorname{polar\_lift}^{2}{\left(a \right)}}} \right)} & \text{otherwise} \end{cases}\right)}{a} & \text{for}\: 2 \left|{\arg{\left(a \right)}}\right| = 0 \wedge \frac{1}{a^{2}} \neq 1 \\\int\limits_{-\infty}^{\infty} \cos{\left(a x \right)} \operatorname{sinc}{\left(x \right)}\, dx & \text{otherwise} \end{cases}$$

Piecewise((pi*Piecewise((0, 1/|a^2| < 1), (a, |a^2| < 1), (meijerg(((1/2,), (0,)), ((0,), (-1/2,)), polar_lift(a)^(-2)), True))/a, (Ne(a^(-2), 1))∧(2*Abs(arg(a)) = 0)), (Integral(cos(a*x)*sinc(x), (x, -oo, oo)), True))