Dear All
Could you please let me know where the formula for computing a beta transform in the picture uploaded exists? Where $i\ge j\ge 1$ are positive integers.
Best regards
Feng Qi (F. Qi)
Dear All
I am preparing an "Acknowledgements" for the revised version of the following preprint. See the picture or the PDF file uploaded. Sorry for my neglect in the first version. Hope to hear your advices soon.
Feng Qi and Bai-Ni Guo, Identities of the Chebyshev polynomials, the inverse of a triangular matrix, and identities of the Catalan numbers, Preprints 2017, 22017030209, 21 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0209.v1 or at http://www.preprints.org/manuscript/201703.0209/v1.
Feng
Dear Anna
I am downloading your PDF file,but failed several times, because the internet speed is too slow today.
You said that you sent a PDF file to me. Do you mean that you sent a PDFfile to my e-mail box? If yes, please let me know which e-mail box you sent the PDF to. Please also tell me your e-mail address here, in order for me to find your e-mail in my e-mail box.
See you later.
Feng
Dear Anna
I downloaded your PDF file above. Please read Remark 6.7, Lemma 2.6, Lemma 2.7, and the proof of Theorem 5.1 in the preprint below. Hope to hear your valuable comments on these.
Feng Qi and Bai-Ni Guo, Identities of the Chebyshev polynomials, the inverse of a triangular matrix, and identities of the Catalan numbers, Preprints 2017, 2017030209, 21 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0209.v1.
Feng
Dear Anna
Before reading the above preprint, don't write. Concretely speaking, your answer to this "Question" had been included in the preprint. Please read Remark 6.7, Lemma 2.6, Lemma 2.7, and the proof of Theorem 5.1 in the preprint. You shouldn't repeat the work again.
Feng
I read you specified paragraphs and found that the presentation of the special function, that I use, relates only t>1. Therefore I suggest another option with development in series, I send a file as an attachment. These results may have you known, they are connected with relatively complex calculations, but will lead to a certain result. Please answer my, I wait Your response with impatient. Your sincerely, Anna Tomova.
Feng Qi, Qing Zou, and Bai-Ni Guo, Some identities and a matrix inverse related to the Chebyshev polynomials of the second kind and the Catalan numbers, Preprints 2017, 2017030209, 25 pages; Available online at http://dx.doi.org/10.20944/preprints201703.0209.v2 or at http://www.preprints.org/manuscript/201703.0209/v2.
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