.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/03_one_loop_integrals.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_03_one_loop_integrals.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_03_one_loop_integrals.py:


One-loop integrals at any precision
===================================

Scalar :math:`B_0` and :math:`C_0` in LoopTools conventions, to double precision
and to 50 digits, and the Method-of-Brackets series for :math:`B_0` compared with
its closed form.

.. GENERATED FROM PYTHON SOURCE LINES 9-26




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    B0(5; 1, 1)          = (1.56959105903599596111056676705 + 1.40496294620814527863127492864j)
    C0(0,0,10; 1, 2, 3)  = (-0.421932531674735453559401494473 - 0.336732268033680194357509591725j)
    C0(0,0,10; 1, 2, 3)  = (-0.421932531674735453559401494473027777240303185 - 0.336732268033680194357509591724866396568161785j)
    B0 closed form       = (1.5695910590359959611105667670493946 + 1.404962946208145278631274928640979j)
    B0 MoB 2F1 series    = (1.5695910590359959611105667670493946 + 1.404962946208145278631274928640979j)
    B0(5;1,2), mu2=91.19^2, delta=1/eps: (10.6675243794782430572441296241 + 0.0j)






|

.. code-block:: Python

    import mpmath as mp

    from ramanujan_qft import B0, B0_mob, C0

    # Double precision: identical to LoopTools 2.16
    print("B0(5; 1, 1)          =", B0(5, 1, 1))            # LoopTools: 1.5695910590 + 1.4049629462i
    print("C0(0,0,10; 1, 2, 3)  =", C0(10, 1, 2, 3))         # LoopTools: -0.4219325317 - 0.3367322680i

    # 50 digits, e.g. to validate another code or for cancellations in large expressions
    print("C0(0,0,10; 1, 2, 3)  =", mp.nstr(C0(10, 1, 2, 3, dps=50), 45))

    # The Method-of-Brackets series gives the same B0, continued across threshold:
    print("B0 closed form       =", mp.nstr(B0(5, 1, 1, dps=40), 35))
    print("B0 MoB 2F1 series    =", mp.nstr(B0_mob(5, 1, dps=40), 35))

    # UV pole and scale: B0 = delta + log(mu^2) + ...
    print("B0(5;1,2), mu2=91.19^2, delta=1/eps:", B0(5, 1, 2, mu2=91.19**2, delta=1))


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.052 seconds)


.. _sphx_glr_download_auto_examples_03_one_loop_integrals.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 03_one_loop_integrals.ipynb <03_one_loop_integrals.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 03_one_loop_integrals.py <03_one_loop_integrals.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 03_one_loop_integrals.zip <03_one_loop_integrals.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_