From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 79803 invoked by alias); 24 Mar 2017 09:20:11 -0000 Mailing-List: contact gsl-discuss-help@sourceware.org; run by ezmlm Precedence: bulk List-Id: List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sourceware.org Received: (qmail 79775 invoked by uid 89); 24 Mar 2017 09:20:10 -0000 Authentication-Results: sourceware.org; auth=none X-Virus-Found: No X-Spam-SWARE-Status: No, score=0.0 required=5.0 tests=AWL,BAYES_20,NO_RDNS_DOTCOM_HELO,RCVD_IN_DNSWL_LOW,RP_MATCHES_RCVD,SPF_PASS autolearn=ham version=3.3.2 spammy=H*r:sk:gsl-dis, H*F:D*verizon.net, H*MI:verizon, H*Ad:D*verizon.net X-HELO: vms173017pub.verizon.net Received: from vms173017pub.verizon.net (HELO vms173017pub.verizon.net) (206.46.173.17) by sourceware.org (qpsmtpd/0.93/v0.84-503-g423c35a) with ESMTP; Fri, 24 Mar 2017 09:20:09 +0000 Received: from vz-proxy-m004.mx.aol.com ([64.236.83.6]) by vms173017.mailsrvcs.net (Oracle Communications Messaging Server 7.0.5.32.0 64bit (built Jul 16 2014)) with ESMTPA id <0ONB006M6B92B3A0@vms173017.mailsrvcs.net> for gsl-discuss@sourceware.org; Fri, 24 Mar 2017 04:19:50 -0500 (CDT) X-CMAE-Score: 0 X-CMAE-Analysis: v=2.2 cv=dNPWoKRb c=1 sm=1 tr=0 a=qxlt2c29UiMP0p6CwArSWg==:117 a=hTZS6uLwhHpx5LOQAS/v3KalXBI=:19 a=IkcTkHD0fZMA:10 a=3RG-kA92mEAA:10 a=6Iz7jQTuP9IA:10 a=HbRCYlVTEPtW7bvfp28A:9 a=QEXdDO2ut3YA:10 Received: by 173.67.5.14 with SMTP id 083fc982; Fri, 24 Mar 2017 09:19:50 GMT To: gsl-discuss@sourceware.org From: Ed Smith-Rowland <3dw4rd@verizon.net> Subject: Debye functions. Message-id: <213cda3e-0b6c-d4bb-ca4c-f868245b791b@verizon.net> Date: Fri, 24 Mar 2017 09:20:00 -0000 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:45.0) Gecko/20100101 Thunderbird/45.7.0 MIME-version: 1.0 Content-type: text/plain; charset=utf-8; format=flowed Content-transfer-encoding: 7bit X-SW-Source: 2017-q1/txt/msg00000.txt.bz2 Greetings, I've been looking at the Debye integrals D_n(x) = \frac{n}{x^n}\int_{0}^{x} \frac{t^n}{e^t - 1}dt The integrand is everywhere positive. The definite integral must be zero for x=0. The values returned by gsl debye functions start at one for x=0 and monotonically decrease. The definite integral of a positive functions must start at zero and monotonically increase. Is it possible that we have a complementary Debye integral? Perhaps scaled? In any case, the functions can't match the formulas in the manual. Thank you. Ed Smith-Rowland