scholarly journals SIGMOIDAL-TYPE SERIES EXPANSION

2008 ◽  
Vol 49 (03) ◽  
pp. 431 ◽  
Author(s):  
BEONG IN YUN
Keyword(s):  
Series Expansion ◽  
Type Series

GAUSS SUMMATION AND RAMANUJAN-TYPE SERIES FOR 1/π

2012 ◽  
Vol 08 (02) ◽  
pp. 289-297 ◽  
Author(s):  
ZHI-GUO LIU
Keyword(s):  
Series Expansion ◽  
Gamma Function ◽  
Hypergeometric Series ◽  
Summation Formula ◽  
Expansion Formula ◽  
Type Series

Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce infinitely many Ramanujan-type series for 1/π.

scholarly journals ON THE q-DERIVATIVE AND q-SERIES EXPANSIONS

2013 ◽  
Vol 09 (08) ◽  
pp. 2069-2089 ◽  
Author(s):  
ZHI-GUO LIU
Keyword(s):  
Series Expansion ◽  
Generating Function ◽  
Series Expansions ◽  
Infinite Products ◽  
Type Series ◽  
Famous Result ◽  
Triangular Numbers

Using a general q-series expansion, we derive some nontrivial q-formulas involving many infinite products. A multitude of Hecke-type series identities are derived. Some general formulas for sums of any number of squares are given. A new representation for the generating function for sums of three triangular numbers is derived, which is slightly different from that of Andrews, also implies the famous result of Gauss where every integer is the sum of three triangular numbers.

Sigmoidal type series expansion

2008 ◽  
Vol 49 ◽  
Author(s):  
Beong In Yun
Keyword(s):  
Series Expansion ◽  
Type Series

Generalized Kantorovich sampling type series on hypergroups

2018 ◽  
Vol 48 (1) ◽  
pp. 117-127
Author(s):  
Seyyed Mohammad Tabatabaie ◽  
A. Sathish Kumar ◽  
Mahmood Pourgholamhossein
Keyword(s):  
Type Series
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