From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 35696 invoked by alias); 25 Mar 2017 21:24:17 -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 33414 invoked by uid 89); 25 Mar 2017 21:24:15 -0000 Authentication-Results: sourceware.org; auth=none X-Virus-Found: No X-Spam-SWARE-Status: No, score=-1.9 required=5.0 tests=BAYES_00,FREEMAIL_FROM,RCVD_IN_DNSWL_NONE,SPF_PASS autolearn=ham version=3.3.2 spammy=Greetings, 998, HTo:U*gsl-discuss X-HELO: mail-wm0-f43.google.com Received: from mail-wm0-f43.google.com (HELO mail-wm0-f43.google.com) (74.125.82.43) by sourceware.org (qpsmtpd/0.93/v0.84-503-g423c35a) with ESMTP; Sat, 25 Mar 2017 21:24:13 +0000 Received: by mail-wm0-f43.google.com with SMTP id t189so15218764wmt.1 for ; Sat, 25 Mar 2017 14:24:13 -0700 (PDT) X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=x-gm-message-state:subject:to:references:from:message-id:date :user-agent:mime-version:in-reply-to:content-transfer-encoding; bh=/1NfHkaeYtAn/OQf7Fp6NlEX6zjk3H3iAhC70NGlXx4=; b=iJ/exS0D7Gq2hCc7BOOPjZvEgcSXlp83q95oJG24y/6UfNymVVX5iCQEENL0tb+EUj kbV1gHiY8W/VON+Y1x455+wSf/ALx2s1bxXMVBkR6Vr7DxpLaBZhdJE0Zych9fTUNFlN +uOZ/JokVwu0SdTyP8PFjPfXq/BUQhPy+ZHBeB6RMF1jzMx6/mg5vX9WzkVfdE4bGqhR L7377L025pYINkCv1tWiYO/IsXj/NBnLCbcto3JTkJE9/xOyjlF8/pgiFOJED9brTuXJ adRF7kClNGui9Q5DOu9AqbblxhS4R9QKyYUAY/v7DRYmnMWUCdPYBo5g1Y/YFQ1y9VAy YM6Q== X-Gm-Message-State: AFeK/H1RXtPqBTqmT1RqhnJQeEQ9Q5RDjXMJZmP5gx/dgMh+dcpJkfwxY8nB0o3ILI1rqw== X-Received: by 10.28.93.194 with SMTP id r185mr3392218wmb.47.1490477051740; Sat, 25 Mar 2017 14:24:11 -0700 (PDT) Received: from [192.168.1.53] (host228-122-dynamic.30-79-r.retail.telecomitalia.it. [79.30.122.228]) by smtp.googlemail.com with ESMTPSA id n14sm8398624wrn.28.2017.03.25.14.24.10 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Sat, 25 Mar 2017 14:24:11 -0700 (PDT) Subject: Re: Debye functions. To: gsl-discuss@sourceware.org References: <213cda3e-0b6c-d4bb-ca4c-f868245b791b@verizon.net> From: maxgacode Message-ID: <70579fe6-ef32-5dac-9918-8f7f21a929a9@gmail.com> Date: Sat, 25 Mar 2017 21:24:00 -0000 User-Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:45.0) Gecko/20100101 Thunderbird/45.8.0 MIME-Version: 1.0 In-Reply-To: <213cda3e-0b6c-d4bb-ca4c-f868245b791b@verizon.net> Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit X-SW-Source: 2017-q1/txt/msg00001.txt.bz2 Il 24/03/2017 10:19, Ed Smith-Rowland ha scritto: > 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. But the 1/x factor goes to zero and so you get a 0/0 indeterminate ratio. Computing the limit to zero returns 1.0! > > The values returned by gsl debye functions start at one for x=0 and > monotonically decrease. Please note the factor \frac{n}{x^n} That factor is the responsible of the observed behavior. > > 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. > I don't think so. Please try to multiply the result of gsl_sf_debye_n(x) by n/x^n and see. Moreover the Chapter 27 of Abramowitz and Stegun (page 998 of my ninth edition) is listing the values of the Debye functions, you can easily verify that GSL implementation is correct. Hope this helps Max