Results 81 to 90 of about 2,958 (201)
Bicomplex Numbers and their Elementary Functions</a> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16"><i>Cubo</i>, 2012 </span><br><span class="r_content">En este artículo introducimos el algebra de números bicomplejos como una generalizacion del campo de números complejos. Describimos como definir funciones elementales en tales algebras (polinomios y funciones exponenciales y trigonometricas) así como sus </span><br><span class="r_sub"><i>M.E LUNA-ELIZARRARÁS<span id="ma_1" style="display:none">, M SHAPIRO, D.C STRUPPA, A VAJIAC</span> <small><a href="#" style="color:#808080;" onClick="return toggle_div(this, 'ma_1')">+3 more</a></small></i></span><br><small><a href="https://doaj.org/article/08a611fe6d0e4a16a3ca5e2214e2ff55" target="_blank" rel="nofollow" title="doaj.org/article/08a611fe6d0e4a16a3ca5e2214e2ff55">doaj</a> </small> <br></div><div class="r"><p class="r_title"><a href="https://doi.org/10.15407/pmach2026.03.008" target="_blank" rel="nofollow">Development of V. L. Rvachev’s Non-Archimedean Calculus</a> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16"><i>Journal of Mechanical Engineering</i></span><br><span class="r_content">This paper was prepared by students of Academician V. L. Rvachev, the creator of non-Archimedean calculus. Structurally, the paper is divided into three sections. The first section examines the relativistic formula for n-ary addition.</span><br><span class="r_sub"><i>Mykola S. Syniekop<span id="ma_2" style="display:none">, Lidiia K. Kravchenko, Tetiana I. Sheiko</span> <small><a href="#" style="color:#808080;" onClick="return toggle_div(this, 'ma_2')">+2 more</a></small></i></span><br><small><a href="https://doaj.org/article/5d594670abd847c18915f2826e9cef06" target="_blank" rel="nofollow" title="doaj.org/article/5d594670abd847c18915f2826e9cef06">doaj</a> </small> <div id="more_2" style="display:none"><a href="/sci_redir.php?doi=10.15407%2Fpmach2026.03.008" target="_blank" rel="nofollow">openaccessbutton.org (pdf)</a><br><a href="javascript:navigator.clipboard.writeText('10.15407/pmach2026.03.008'); alert('Copied the doi');">copy doi</a> <small>(10.15407/pmach2026.03.008)</small><br></div><small><a href="#" onClick="return toggle_div(this, 'more_2')">+1 more source</a></small><br></div><div class="r"><p class="r_title"><a href="https://doi.org/10.13140/rg.2.2.11588.27527" target="_blank" rel="nofollow">Formulae for the exponential, the hyperbolic and the trigonometric functions in terms of the logarithmic function</a> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16">, 1991 </span><br><span class="r_content">A common definition of the exponential function is as the inverse function of the logarithmic function, which is defined as the definite integral of the rational function 1/t over the interval [1,x] with x > 0. The hyperbolic functions (hyperbolic sine, cosine, tangent, etc.) are next defined in terms of the exponential function.</span><br><span class="r_sub"><i>Ioakimidis, Nikolaos<span id="ma_3" style="display:none">, Anastasselou, Eleni</span> <small><a href="#" style="color:#808080;" onClick="return toggle_div(this, 'ma_3')">+1 more</a></small></i></span><br><small><a href="https://explore.openaire.eu/search/publication?pid=10.13140%2Frg.2.2.11588.27527" target="_blank" rel="nofollow" title="openaire.eu/search/publication?pid=10.13140%2Frg.2.2.11588.27527">openaire</a> </small> <div id="more_3" style="display:none"><a href="/sci_redir.php?doi=10.13140%2Frg.2.2.11588.27527" target="_blank" rel="nofollow">openaccessbutton.org (pdf)</a><br><a href="https://hdl.handle.net/10889/10842" target="_blank" rel="nofollow" title="hdl.handle.net/10889/10842">hdl.handle.net</a><br> <a href="javascript:navigator.clipboard.writeText('10.13140/rg.2.2.11588.27527'); alert('Copied the doi');">copy doi</a> <small>(10.13140/rg.2.2.11588.27527)</small><br></div><small><a href="#" onClick="return toggle_div(this, 'more_3')">+2 more sources</a></small><br></div><div class="r"><p class="r_title"><a href="https://core.ac.uk/download/655522755.pdf" target="_blank" rel="nofollow">Complex Functions Examples c-3: Elementary Analytic Functions and Harmonic Functions</a> <b><a href="https://core.ac.uk/download/655522755.pdf" target="_blank" rel="nofollow">[PDF]</a></b> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16">, 2008 </span><br><span class="r_content">This is the third textbook containing examples from the Theory of Complex Functions. Some of the topics are examples of elementary analytic functions, like polynomials, fractional functions, exponential functions and the trigonometric and the hyperbolic ...</span><br><span class="r_sub"><i>Mejlbro, Leif</i></span><br><small><a href="https://core.ac.uk/works/276517358" target="_blank" rel="nofollow" title="core.ac.uk/works/276517358">core</a> </small> <br></div><div class="r"><p class="r_title"><a href="" target="_blank" rel="nofollow">Complex exponential and logarithm functions</a> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16">, 2014 </span><br><span class="r_content">Educação Superior::Ciências Exatas e da Terra::MatemáticaThe complex exponential and logarithm functions can be visualized by looking at the real and imaginary part of the function and its absolute value.</span><br><span class="r_sub"><i>Goriely, Alain, Morris, Rob</i></span><br><small><a href="https://core.ac.uk/works/337338033" target="_blank" rel="nofollow" title="core.ac.uk/works/337338033">core</a> </small> <br></div><div class="r"><p class="r_title"><a href="" target="_blank" rel="nofollow">Using Differentials to Differentiate Trigonometric and Exponential Functions</a> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16">, 2020 </span><br><span class="r_content">Differentiating a polynomial is easy. To differentiate u 2 with respect to u, start by computing and then dropping the last term, an operation that can be justified in terms of limits. Differential notation, in general, can be regarded as a shorthand for </span><br><span class="r_sub"><i>Tevian Dray</i></span><br><small><a href="https://core.ac.uk/works/100861884" target="_blank" rel="nofollow" title="core.ac.uk/works/100861884">core</a> </small> <br></div><div class="r"><p class="r_title"><a href="" target="_blank" rel="nofollow">Geometrical logarithmic and trigonometric hypercomplex functions of quaternionic type</a> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16">, 2011 </span><br><span class="r_content">Quaternionic theory has greatly been developed in recent years [1-12]. Thus, in our view, the study of trigonometric and logarithmic type quaternionic functions is important for the determination and realization of a hyper complex theory.</span><br><span class="r_sub"><i>Coelho, J., Borges, M. F., Marão, J. A.</i></span><br><small><a href="https://core.ac.uk/works/291182532" target="_blank" rel="nofollow" title="core.ac.uk/works/291182532">core</a> </small> <div id="more_7" style="display:none"><a href="https://core.ac.uk/works/337638262" target="_blank" rel="nofollow" title="core.ac.uk/works/337638262">core.ac.uk</a><br><a href="https://core.ac.uk/works/162363611" target="_blank" rel="nofollow" title="core.ac.uk/works/162363611">core.ac.uk</a><br></div><small><a href="#" onClick="return toggle_div(this, 'more_7')">+2 more sources</a></small><br></div><div class="r"><p class="r_title"><a href="https://doi.org/10.1090/s0002-9939-1976-0414871-2" target="_blank" rel="nofollow">Inequalities for entire functions of exponential type</a> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16">, 1976 </span><br><span class="r_content">This paper is concerned with a class of linear operators acting in the space of the trigonometric polynomials and preserving the inequalities of the form
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</span><br><span class="r_sub"><i>T. Genchev</i></span><br><small><a href="https://core.ac.uk/works/181544077" target="_blank" rel="nofollow" title="core.ac.uk/works/181544077">core</a> </small> <div id="more_8" style="display:none"><a href="/sci_redir.php?doi=10.1090%2Fs0002-9939-1976-0414871-2" target="_blank" rel="nofollow">openaccessbutton.org (pdf)</a><br><a href="javascript:navigator.clipboard.writeText('10.1090/s0002-9939-1976-0414871-2'); alert('Copied the doi');">copy doi</a> <small>(10.1090/s0002-9939-1976-0414871-2)</small><br></div><small><a href="#" onClick="return toggle_div(this, 'more_8')">+1 more source</a></small><br></div><div class="r"><p class="r_title"><a href="https://doi.org/10.3389/fams.2025.1568834" target="_blank" rel="nofollow">New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equations</a> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16"><i>Frontiers in Applied Mathematics and Statistics</i></span><br><span class="r_content">The purpose of this article is to explore a new method for solving one of the nonlinear partial differential equations (NPDE) which is difficult to solve.</span><br><span class="r_sub"><i>Nathanon Sribua-Iam<span id="ma_9" style="display:none">, Settapat Chinviriyasit</span> <small><a href="#" style="color:#808080;" onClick="return toggle_div(this, 'ma_9')">+1 more</a></small></i></span><br><small><a href="https://doaj.org/article/9b9ee7e46437494fbad69dedba43989f" target="_blank" rel="nofollow" title="doaj.org/article/9b9ee7e46437494fbad69dedba43989f">doaj</a> </small> <div id="more_9" style="display:none"><a href="/sci_redir.php?doi=10.3389%2Ffams.2025.1568834" target="_blank" rel="nofollow">openaccessbutton.org (pdf)</a><br><a href="javascript:navigator.clipboard.writeText('10.3389/fams.2025.1568834'); alert('Copied the doi');">copy doi</a> <small>(10.3389/fams.2025.1568834)</small><br></div><small><a href="#" onClick="return toggle_div(this, 'more_9')">+1 more source</a></small><br></div><div class="r"><p class="r_title"><a href="https://doi.org/10.1007/bf02247945" target="_blank" rel="nofollow">The Durand-Kerner method for trigonometric and exponential polynomials - Das Durand-Kerner-Verfahren für trigonometrische und exponentielle Polynome</a> </p><span class="r_subtitle"><img src="/img/openaccess.ico" alt="open access: yes" title="open access: yes" width="16" height="16">, 1988 </span><br><span class="r_content">The problem of finding all roots of an exponential or trigonometric equation is reduced to the determination of zeros of algebraic polynomials where the well-known Durand-Kerner algorithm can be applied.</span><br><span class="r_sub"><i>Weidner, P.</i></span><br><small><a href="https://core.ac.uk/works/128164797" target="_blank" rel="nofollow" title="core.ac.uk/works/128164797">core</a> </small> <div id="more_10" style="display:none"><a href="/sci_redir.php?doi=10.1007%2Fbf02247945" target="_blank" rel="nofollow">openaccessbutton.org (pdf)</a><br><a href="javascript:navigator.clipboard.writeText('10.1007/bf02247945'); alert('Copied the doi');">copy doi</a> <small>(10.1007/bf02247945)</small><br></div><small><a href="#" onClick="return toggle_div(this, 'more_10')">+1 more source</a></small><br></div><div class="r"><div style="margin-bottom:2px;overflow:hidden"><div style="display: inline-block; float: left; font-size: small; padding-right: 16px; margin-top: -1px; padding-bottom: 1px;"><a href="/q-mathematics/" class="suggestion"onclick="show_loader();"><b>mathematics</b></a><br/><a href="/q-laplace_transform/" class="suggestion"onclick="show_loader();"><b>laplace transform</b></a><br/><a href="/q-trigonometric_functions/" class="suggestion"onclick="show_loader();"><b>trigonometric functions</b></a><br/></div><div style="display: inline-block; float: left; font-size: small; padding-right: 16px; margin-top: -1px; padding-bottom: 1px;"><a href="/q-trigonometric_function/" class="suggestion"onclick="show_loader();"><b>trigonometric function</b></a><br/><a href="/q-monotonically_increasing_function/" class="suggestion"onclick="show_loader();"><b>monotonically increasing function</b></a><br/><a href="/q-monotonically_decreasing_function/" class="suggestion"onclick="show_loader();"><b>monotonically decreasing function</b></a><br/></div><div style="display: inline-block; float: left; font-size: small; padding-right: 16px; margin-top: -1px; padding-bottom: 1px;"><a href="/q-fos%3A_mathematics/" class="suggestion"onclick="show_loader();"><b>fos: mathematics</b></a><br/><a href="/q-numerical_inversion/" class="suggestion"onclick="show_loader();"><b>numerical inversion</b></a><br/><a href="/q-rational_approximation/" class="suggestion"onclick="show_loader();"><b>rational approximation</b></a><br/></div></div></div><div class="pagenav"><a href="/q-exponential_and_trigonometric_functions/p-8/" rel="nofollow"><b>previous</b></a> <a href="/q-exponential_and_trigonometric_functions/p-7/" rel="nofollow">7</a> <a href="/q-exponential_and_trigonometric_functions/p-8/" rel="nofollow">8</a> <b>9</b> <a href="/q-exponential_and_trigonometric_functions/p-10/" rel="nofollow">10</a> <a href="/q-exponential_and_trigonometric_functions/p-11/" rel="nofollow">11</a> <a href="/q-exponential_and_trigonometric_functions/p-10/" id="next" rel="nofollow"><b>next</b></a> </div><br></div>
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