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CERTAIN FORMULAS INVOLVING A MULTI-INDEX MITTAG-LEFFLER FUNCTION
Bansal, Manish Kumar,Harjule, P.,Choi, Junesang,Mubeen, Shahid,Kumar, Devendra The Youngnam Mathematical Society 2019 East Asian mathematical journal Vol.35 No.1
Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati's work, we aim to investigate a generalized multi-index Mittag-Leffler function and, among possible numerous formulas, choose to present several formulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.
Bansal, Manish Kumar,Kumar, Devendra,Jain, Rashmi Department of Mathematics 2019 Kyungpook mathematical journal Vol.59 No.3
In this work, we evaluate the Mellin transform of the Marichev-Saigo-Maeda fractional integral operator with Appell's function $F_3$ type kernel. We then discuss six special cases of the result involving the Saigo fractional integral operator, the $Erd{\acute{e}}lyi$-Kober fractional integral operator, the Riemann-Liouville fractional integral operator and the Weyl fractional integral operator. We obtain new and known results as special cases of our main results. Finally, we obtain the images of S-generalized Gauss hypergeometric function under the operators of our study.
Right Atrial Paraganglioma: An Extremely Rare Primary Cardiac Neoplasm Mimicking Myxoma
Ashok Garg,Deepika Mishra,Manish Bansal,Hari Ram Maharia,Vikram Goyal 한국심초음파학회 2016 Journal of Cardiovascular Imaging (J Cardiovasc Im Vol.24 No.4
In this report, we present a case of 35-year-old lady who had presented with atypical chest pain and exertional breathlessness forpast six months. Transthoracic and transesophageal echocardiograms showed a well-circumscribed, echo-dense mass in the rightatrium, attached to the interatrial septum at the level of atrioventricular junction and in the vicinity of coronary sinus ostium. Sheunderwent successful resection of the cardiac mass. Histopathology revealed paraganglioma, which was reconfirmed by immunohistochemistrystudy. This represents an extremely rare presentation as primary cardiac tumors are 20-times less common thanmetastatic tumors and paraganglioma is one of the rarest primary cardiac tumors, accounting for < 1% of all cases.
Certain formulas involving a multi-index Mittag-Leffler function
P. Harjule,최준상,Manish Kumar Bansal,Shahid Mubeen,Devendra Kumar 영남수학회 2019 East Asian mathematical journal Vol.35 No.1
Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati’s work, we aim to investigate a generalized multi-index Mittag-Leffler func- tion and, among possible numerous formulas, choose to present several for- mulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.
Shahi Pratyush,Chadha Manish,Sehgal Apoorv,Sudan Aarushi,Meena Umesh,Bansal Kuldeep,Batheja Dheeraj 대한척추외과학회 2022 Asian Spine Journal Vol.16 No.3
Study Design: Cross-sectional study.Purpose: To evaluate sagittal balance, pulmonary function, and spinopelvic parameters in patients with healed spinal tuberculosis with severe thoracic kyphosis.Overview of Literature: Deterioration of neurological function is an absolute indication of surgical intervention in severe post-tubercular kyphosis, but the relationship of compromise in lung function and spinal alignment with severity of kyphosis is still unclear.Methods: Twenty patients (age, 14–60 years) with healed spinal tuberculosis with thoracic kyphosis >50° were included. Lateral-view radiography of the whole spine, including both hips, was performed for assessment of kyphotic angle (K angle), sagittal balance, lumbar lordosis, and spinopelvic parameters. Pulmonary function was assessed by measuring the forced vital capacity (FVC), forced expiratory volume in 1 second (FEV1), and their ratio (FEV1/FVC) by spirometry.Results: A positive correlation between severity of kyphosis and sagittal imbalance was noted, with compensatory mechanisms maintaining the sagittal balance in only up to 80° of dorsal kyphosis. In >80° of kyphosis, FVC was found to be markedly decreased (mean FVC=50.6%). The mean K angle was lower in subjects with lower thoracic kyphosis. In lower thoracic kyphosis, due to short lordotic and long kyphotic curves, both lumbar lordosis and pelvic retroversion worked at compensation, whereas, in middle thoracic kyphosis, due to long lordotic curve, only lumbar lordosis was required. Normal pulmonary function (mean FVC, 83.0%) and lesser kyphotic deformity (mean K angle in adolescents, 69.8°; in adults, 94.4°) were found in adolescents.Conclusions: In >80° of thoracic kyphosis, there is sagittal imbalance and a markedly affected pulmonary function. Such patients should be offered corrective surgery if they are symptomatic and medically fit to undergo the procedure. However, whether the surgical procedure would result in improved pulmonary function and sagittal balance needs to be evaluated by a follow-up study.