# [seqfan] Mathematical "≺" .

CLAUDE DEQUATRE claude.dequatre57 at yahoo.com
Mon Oct 23 15:31:58 CEST 2023

```>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
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