On the Solution of Definite Integrals Occurring in Antenna Theory

1944 ◽  
Vol 15 (12) ◽  
pp. 840-841 ◽  
Author(s):  
Sidney Weinbaum
2019 ◽  
Vol 10 (1) ◽  
pp. 222-237
Author(s):  
M. I. Qureshi ◽  
Kaleem A. Quraishi ◽  
Dilshad Ahamad

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1453
Author(s):  
Robert Reynolds ◽  
Allan Stauffer

In this present work we derive, evaluate and produce a table of definite integrals involving logarithmic and exponential functions. Some of the closed form solutions derived are expressed in terms of elementary or transcendental functions. A substantial part of this work is new.


1903 ◽  
Vol 71 (467-476) ◽  
pp. 97-101 ◽  

The expansion of a function f(θ) of an angle θ varying between 0 and π in terms of a series proceeding by the sines of the multiples of θ depends on the fundamental theorem, ∫ π 0 sin pθ sin qθ dθ = 0, where p and q are integer numbers not equal to each other.


2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Xin Chen ◽  
Victor Taracila ◽  
Timothy Eagan ◽  
Hiroyuki Fujita ◽  
Xingxian Shou ◽  
...  

We suggest that center-fed dipole antenna analytics can be employed in the optimized design of high-frequency MRI RF coil applications. The method is illustrated in the design of a single-segmented birdcage model and a short multisegmented birdcage model. As a byproduct, it is shown that for a long single-segmented birdcage model, the RF field within it is essentially a TEM mode and has excellent planar uniformity. For a short shielded multisegmented birdcage model, the RF field is optimized with a target-field approach with an average SAR functional. The planar homogeneity of the optimized RF field is significantly improved compared with that of a single-segmented birdcage model with the same geometry. The accuracy of the antenna formulae is also verified with numerical simulations performed via commercial software. The model discussed herein provides evidence for the effectiveness of antenna methods in future RF coil analysis.


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