Heard JH plans new edition of Examples of Finite Differences [1820]. Will send list of errors HW found in original. Results of HW's investigation of self-repeating series of numbers.
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Heard JH plans new edition of Examples of Finite Differences [1820]. Will send list of errors HW found in original. Results of HW's investigation of self-repeating series of numbers.
Recalls JH's predecessor [Isaac Newton] at Mint was also interested in Bernoulli's 'Isoperimetrical Problems.' HW plans paper on new expression for coefficients of differences of zero in self-repeating series.
Cambridge [Philosophical] Society will publish HW's paper on self-repeating series. Suggests JH clarify some equations in new edition of [Examples of Finite Differences (1820)].
Additional suggestions for improving clarity of equations in new edition of JH's [Examples of Finite Differences (1820)].
Additional improvements for new edition of JH's [Examples of Finite Differences (1820)].
Further discussion of need for two constants [see HW's 1854-[5]-11]. Sends first installment of errata HW found in JH's [Examples of Finite Differences (1820)]. Realizes JH's duties [at Mint] afford little time to publish new edition. Suggests printing only errata list to first edition.
Sends copy of HW's paper, with manuscript listing properties of differences of zero. Is there a published table of such differences like that in JH's [Examples of Finite Differences (1820)]?
Learned to simplify expression for Bernoulli's number B=2n+1 using JH's formula.
Happy that JH may be leaving Mint and returning to scientific pursuits. HW resumed work on equations in finite differences. Hopes to reconcile discrepancy between JH's and P. S. Laplace's solutions. JH's solution renders only particular, not general, solutions.
Approves of JH sharing HW's findings. HW on excellent terms with Augustus De Morgan. Suspects two integrals exist, one real and one imaginary, for P. S. Laplace's equation.
Testing recent work on equations analogous to P. S. Laplace's but of higher order. Solution so simple that HW expects to find it published elsewhere. Corrects error in previous letter regarding generality of arbitrary constants.
Demonstrates easier way to treat equations analogous to P. S. Laplace's.
Please correct error in HW's earlier calculations.