19 | On transcendental progressions, that is, those whose general terms cannot be given algebraically |
20 | The summation of an innumerable progression |
25 | A general method for summing series |
41 | On the sums of series of reciprocals |
43 | On harmonic progressions |
46 | Universal methods of series |
47 | Finding the sum of any series from a given general term |
55 | Universal method for summation of series, further developed |
61 | On sums of series of reciprocals from powers of natural numbers from another discussion, in which the sums are derived principally from another source |
63 | Demonstration of the sum of the series 1 + 1/4 + 1/9 + 1/16 … |
71 | A dissertation on continued fractions |
72 | Various observations about infinite series |
74 | On various methods for expressing the quadrature of a circle with verging numbers |
122 | On products created from infinite factors |
123 | Observations on continued fractions |
125 | Consideration of a progression suitable for finding the quadrature of a circle |
128 | An easy method for computing the natural and artificial sines and tangents of angles |
130 | Considerations on certain series |
189 | On the determination of series, or a new method for finding the general terms of series |
190 | Consideration of certain series which are gifted with particular properties |
246 | A contribution to the calculations of sines |
247 | On divergent series |
275 | Annotations to a certain passage of Descartes for finding the quadrature of the circle |
280 | On progressions of arcs of circles, of which the accompanying tangents proceed by a certain law |
281 | A specimen of a singular algorithm |
326 | Analytical observations |
352 | Remarks on a beautiful relation between direct as well as reciprocal power series |
393 | On the sum of series involving the Bernoulli numbers |
432 | Analytical exercises |
447 | The summation of the progressions sin(φ^{λ}) + sin(2φ^{λ}) + sin(3φ^{λ}) + ... + sin(nφ^{λ}); cos(φ^{λ}) + cos(2φ^{λ}) + cos(3φ^{λ}) + ... + cos(nφ^{λ}). |
453 | Eminent properties of series within which the general term is contained as x = (1/2)(a+b/√k)(p+q√k)^{n} + (1/2)(a-b/√k)(p-q√k)^{n} |
465 | A demonstration of a theorem of Newton on the expansion of the powers of a binomial by cases, in which the exponents are not integral numbers |
477 | Meditations about a singular type of series |
489 | On unravelling exponential formulas |
507 | On the infinity of infinities of orders of the infinitely large and infinitely small |
522 | On the formation of continuous fractions |
550 | On series in which the product of two consecutive terms make a given progression |
551 | Various methods for inquiring into the innate characters of series |
553 | Analytical observations |
555 | An examination of the use of interpolating methods in the doctrine of series |
561 | Various observations about angles proceeding in geometric progression |
562 | On how sines and cosines of multiplied angles may be expressed by products |
565 | On highly transcendental quantities, which may not be expressed in any way by integral formulas |
575 | De mirabilibus proprietatibus unciarum, quae in evolutione binomii ad potestatem quamcunqua evecti occurrunt |
583 | De numero memorabili in summatione progressionis harmonicae naturalis occurrente |
584 | De insignibus proprietatibus unciarum binomii ad uncias quorumvis polynomiorum extensis |
592 | On the resolution of transcendental fractions into infinitely many simple fractions |
593 | On the transformation of series into continued fractions, where at once this not mediocre theory is enlarged |
597 | A new and most easy method for summing series of reciprocals of powers |
613 | Dilucidationes in capita postrema calculi mei differentalis de functionibus inexplicabilibus |
616 | On the transformation of the divergent series 1 - mx + m(m+n)x^{2} - m(m+n)(m+2n)x^{3} + etc. into a continued fraction |
617 | On the summation of series, in which the signs of the terms alternate |
636 | On the multiplication of angles which are to be obtained by factors |
637 | A new demonstration, with respect to which prevails the expansion of binomial powers by Newton even by fractional exponents |
642 | On a singular rule for differentiating and integrating, which occurs in the sums of series |
652 | On the general term of hypergeometric series |
655 | General observations about series, of which the terms arising for the sines or cosines of multiplied angles come forth |
661 | Several considerations about hypergeometric series |
663 | Plenior expositio serierum illarum memoragilium, quae ex unciis potestatum binomii formantur |
664 | Analytical exercises |
684 | On the roots of the infinite equation 0 = 1 - (xx)/(n(n+1)) + (x^{4})/(n(n+1)(n+2)(n+3)) - (x^{6})/(n.....(n+5)) + etc. |
685 | An analytical exercise, where in particular a most general summation of series is given |
686 | Elucidations about the formula, in which the sines and cosines of angles are to be multiplied, where at once large difficulties are diluted |
703 | An easy method for finding series proceeding by the multiplication of the sines and cosines of angles, of which the use in the universal theory of astronomy is very great |
704 | Disquisitio ulterior super seriebus secundum multipla cuiusdam anguli progredientibus |
705 | Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae |
706 | On a new type of rational and highly convergent series, by which the ratio of the periphery to the diameter is able to be expressed |
709 | On the expansion of the power of any polynomial 1 + x + x^{2} + x^{3} + x^{4} + etc. |
710 | Example of the transformation of singular series |
722 | Analytical disquisitions on the expansion of the trinomial power (1+x+xx)^{n} |
726 | A demonstration of a notable theorem of numbers a twelfth part of binomial powers |
736 | On the summation of series contained in the form a/1 + a^{2}/4 + a^{3}/9 + a^{4}/16 + a^{5}/25 + a^{6}/36 + etc. |
742 | Observations about continued fractions contained in the form S = n/(1+(n+1)/(2+(n+2)/(3+(n+3)/(4+etc.)))) |
743 | De serie maxime memorabili, qua potestas binomialis quaecunque exprimi potest |
745 | On the continued fractions of Wallis |
746 | A method for gathering the sums of infinite series by investigating differential formulas |
747 | On remarkable series, by which the sines and cosines of multiplied angles may be expressed |
750 | A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers |
768 | De unciis potestatum binomii earumque interpolatione |
809 | Series maxime idoneae pro circuli quadratura proxime invenienda |
810 | Enodatio insignis cuiusdam paradoxi circa multiplicationem angulorum observati |
819 | Continuation of some fragments taken from the Mathematics day book |