scholarly journals Some new linear relations for odd degree polynomial splines at mid-points

1983 ◽  
Vol 59 (1) ◽  
pp. 24-25 ◽  
Author(s):  
Manabu Sakai
Keyword(s):  
Polynomial Splines ◽  
Degree Polynomial ◽  
Linear Relations ◽  
Odd Degree

On the question of whether f″+ e−zf′ + B(z)f = 0 can admit a solution f ≢ 0 of finite order

1986 ◽  
Vol 102 (1-2) ◽  
pp. 9-17 ◽  
Author(s):  
Gary G. Gundersen
Keyword(s):  
Entire Function ◽  
Finite Order ◽  
Infinite Order ◽  
Independent Interest ◽  
Partial Result ◽  
Transcendental Entire Function ◽  
Degree Polynomial ◽  
Odd Degree ◽  
Polynomial Of Odd Degree

SynopsisWe show that if B(z) is either (i) a transcendental entire function with order (B)≠1, or (ii) a polynomial of odd degree, then every solution f≠0 to the equation f″ + e−zf′ + B(z)f = 0 has infinite order. We obtain a partial result in the case when B(z) is an even degree polynomial. Our method of proof and lemmas for case (i) of the above result have independent interest.

scholarly journals Explicit energy expansion for general odd-degree polynomial potentials

2013 ◽  
Vol 88 (5) ◽  
pp. 055004 ◽  
Author(s):  
Asiri Nanayakkara ◽  
Thilagarajah Mathanaranjan
Keyword(s):  
Degree Polynomial ◽  
Odd Degree ◽  
Polynomial Potentials ◽  
Energy Expansion
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