[seqfan] Mathematical "≺" .

[CLAUDE DEQUATRE]

>From C. Dequatre.
To: Sean.A Irvine.
     Richard Mathar.
     Arthur O' Dwyer.
Reference: my e-mail to SeqFan List of Oct 19, 2023.

                                                                                              Dear all,

Following Sean's suggestion, I emailed Dr Shamos.  Answering my question about the meaning of the symbol "≺", his response is given below:
"The symbol < with curved edges means "has the asymptotic expansion."  Often the symbol used is ~, but that is ambiguous because it also means "approximately equal to."  It is indeed true that Sum[(-1)^(k+1)Binomial[2k,k]/(2k-1),{k,1,Infinity}] diverges.  However, consider Sum[(-1)^(k+1)x^k*Binomial[2k,k]/(2k-1),{k,1,Infinity}], which has the formal sum Sqrt[4x+1]-1.  Now let x = 1, and the result is Sqrt[5]-1."

Dr Shamos also informed me that a new edition of the Catalog of the Real Numbers is coming out this fall with far more
entries, all in Mathematica, with more decimal digits for each.


I would like to thank you all again for your help.

                                                                                                        Best Regards.

                                                                                                                    C. Dequatre

                                                                                                                    E-mail: claude.dequatre57 at yahoo.com