• 충청수학회지
• /
• 제24권4호
• /
• pp.745-758
• /
• 2011

Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.

• 대한수학회논문집
• /
• 제27권2호
• /
• pp.257-264
• /
• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• 대한수학회논문집
• /
• 제33권4호
• /
• pp.1239-1248
• /
• 2018

Recently, many authors have obtained several hypergeometric identities involving hypergeometric functions of one and multi-variables such as the Appell's functions and Horn's functions. In this paper, we obtain several new transformations suitably by applying the fractional calculus operator to these hypergeometric identities, which was introduced recently by Tremblay.

• 대한수학회논문집
• /
• 제38권3호
• /
• pp.807-819
• /
• 2023

In 2019, Mathur and Solanki [7, 8] obtained a few transformation formulas for Appell, Horn and the Kampé de Fériet functions. Unfortunately, some of the results are well-known and very old results in literature while others are erroneous. Thus the aim of this note is to provide the results in corrected forms and some of the results have been written in more compact form.

• 호남수학학술지
• /
• 제32권3호
• /
• pp.389-397
• /
• 2010

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

• 호남수학학술지
• /
• 제27권4호
• /
• pp.603-608
• /
• 2005

In 1999 and 2003, Padmanabham established two results (one each) for Exton's triple hypergeometric series $X_8$. We aim at showing that Exton's later result can be derived from his former one.

• 대한수학회논문집
• /
• 제23권2호
• /
• pp.187-189
• /
• 2008

We aim at presenting an interesting result for a reducibility of Exton's triple hypergeometric series $X_2$. The identity to be given here is obtained by combining Exton's Laplace integral representation for $X_2$ and Henrici's formula for the product of three hypergeometric series.

• 대한수학회논문집
• /
• 제24권4호
• /
• pp.517-521
• /
• 2009

The object of this note is to derive Padmanabham's transformation formula for Exton's triple hypergeometric series $X_8$ by using a different method from that of Padmanabham's. An interesting special case is also pointed out.

• Journal of Ship and Ocean Technology
• /
• 제8권3호
• /
• pp.18-25
• /
• 2004

Sound reception system is required to detect the sound and the quadrantal direction of the other ship's horn sound, to overcome the effects of enclosed wall for navigation space, functioning as a sound barrier. However, the realized systems can only provide quadrantal information of the other ship. This paper presents a new arrangement of microphones, having geometrically symmetric deployment with the same distances between sensors and the same angles between adjacent sensors with respect to the geometrical center. The sound pressures received at microphones are transformed into the related envelope signals by applying Hilbert transform. The time delays between microphones are estimated by the correlation functions between the derived envelope signals. This envelope base processing mitigates the noises related to the reflection by ship and sea surface. Then, the directional information is easily defined by using the estimated time delays. The suggested method is verified by the generated signals using boundary element method for a small ship model with sea surface wave. The estimated direction is quite similar to the true one and therefore the proposed approach can be used as an efficient sound reception system.

• The Journal of Korean Physical Therapy
• /
• 제8권1호
• /
• pp.109-119
• /
• 1996

Although the physical therapy of both East and West has been based on an identical philosophy, they have had their own therapy with difference in its form and pattern. In general, cupping is used to diagnose and treat viscera by means of acupuncture point, and myofascial release is also used for both diagnosis and orthopedic treatment on the basis of trigger point and myofascial however, when they have a lot of identical facts such as using both mental and physical aspects of human beings for treatment, keeping nervous action balanced, and recovering depressed nervous functions and relieving the pain. In addition. their identical fact includes that they tend to treat patients by using symptoms and reaction shown in their skin, and that both East and West try to consider myofascia as an integrated totality and as a unified body of organic functions with correlations. Among the principles of myofascial release, recently, it has been very identical that stimulus given to the skin results in synapse to sympathetic nerve through dosal horn cell has an effect on viscera, and that cupping is sued for diagnosis and treatment of viscera. It is required, therefore, to continue to carry out studying on this field.