The RLH Equation

 Here is a mathematical idea, that I have recently stipulated. Although I am not super confident that this is to a tee; I will let you know what I have come up with here, and we'll give it a shot:

The natural log of [[The summation from N = 0 to infinity, of [(e^(N+3)/e^(2N)]] TIMES

                                                                           [[PI TIMES [The natural log of PI]/2]] TIMES

         [[1/[[INVERSE ZETA OF ZERO] TIMES THE NATUAL LOG OF [THE SUMMATION FROM N = 0 TO INFINITY, OF [[I TIMES PI]/e^(2N-1)]]}]

= 0 +1+2+3... =  {~ INFINITY (FOR A EUCLIDEAN-RELATED EXPANSION), OR, (-1/12) (FOR A CLIFFORD-RELATED EXPANSION}. 

I CALL THIS EQUATION, THE "RHL" EQUATION.

PLEASE LET ME KNOW HOW I DID. FEEL FREE TO COMMENT! IF THERE'S A MISTAKE, PLEASE TELL ME WHAT YOU PERCEIVE. THANK YOU FOR YOUR READERSHIP! SINCERELY, SAMUEL DAVID ROACH. TO BE CONTINUED!                                                              

A Perception As To A View Of "Departure" Versus A Perception As To A View Of "Approach" (An Editorial)

 I perceive, that when the Zeta Function is set to "-i*(e^2)," that the directly corresponding Bessel Function, thus formed, will consequently be equal to "0."

Therefore; it follows then, that -- 

If one were to work to metaphorically define the "Departure," of what "moves" in the "direction" or "manner," of working to form the permittivity, of pressurizing the general eluded-to pure vacuum, -- that was here to exist, directly prior to the Action of the "Big-Bang," to tend to be:

[The eigenfunction "value" of {The Natural Log of {The Natural Log of (the hyperbolic sine of (-i*(e^2)));] which may be termed of as:

[The eigenfunction "value" of {ln(ln(sin(h)((Zeta^(-1)(0)))}]; ----

That; the directly corresponding metaphorical "Approach," of what "moves" in the "direction" or "manner," of working to form the impedance, of pressurizing the general eluded-to pure vacuum, -- that was here to exist, directly prior to the Action of the "Big-Bang," would thereby consequently tend to be:

[The eigenfunction "value" of {The Negative of the Natural Log of {The Natural Log of (the hyperbolic cosine of (-i(e^2)))]; which may be termed of as:

[The eigenfunction "value" of {-ln(ln(cos(h)((Zeta^(-1)(0))))}]. -- Please let me know what you think!

I will continue with the suspense later! To Be Continued! Sincerely, SAMUEL DAVID ROACH. (1989).

Coupling Of Equal And Opposite Holomorphic-Related Wave-Tug

Let us initially consider a discrete quantum of energy, that is here to be moving in the relative forward-holomorphic direction, in a euclidean-related manner, via a unitary Lagrangian, that is over a discrete increment of time.  Let us here consider in this particular case, that this one inferred discrete quantum of energy alone -- is here to simply be the overall energy of the system of this given arbitrary respective "case."  Next -- let's consider what was earlier stated, to be acting as the relative forward-holomorphic direction, to be of a Lagrangian-based directorial path, that may here arbitrarily be considered as heading into the relative "i" direction, over the earlier inferred discrete increment of time.  Since the said discrete increment of energy, is here to be the overall energy of the here mentioned respective given arbitrary system of such a particular case, one may then consider that the inferred discrete quantum of energy, is here to be considered as being the respective given arbitrary Hamiltonian Operator.  Furthermore -- the kinematic energy, when this is here to be taken as being the actual motion of this said respective Hamiltonian Operator, as taken over an evenly-gauged Hamiltonian operand, -- may here be considered as being the Lagrangian of this given arbitrary respective system of kinematic motion, over time.  {To paraphrase, as in accordance with Newton's Laws of Physics; for every action, there is an equal and opposite reaction, -- to where such an implied opposite "reaction," is here to be applied in the opposite direction from the initially stated action of such a general case.}  Consequently; As the implied discrete quantum of energy, that is here to be acting as the respective Hamiltonian Operator, is to be traveling in the relative "i" direction (which is here to be in the relative forward-holomorphic direction, or, to the relative "left"), -- there is an equal and opposite reaction of the space-time-fabric itself, that is here to be of the topological substrate of the earlier so-eluded-to Hamiltonian operand, that is here to be directed in the relative "-i" direction, -- upon the kinematic action of the said discrete quantum of energy's motion, as it is here to be traveling in the general manner of its innate tendency of directorial topological sway of wave-related tug.  Remember when I had mentioned in similar but different words, -- that the convergence of mini-stringular segmentation, upon those first-order point particles that work to comprise a superstring of discrete energy permittivity, is to tend to bear a relatively hyperbolic approach, towards that particular general genus of a cotangent bundle, that is indicative of the nature of superstringular Ward-Cauchy-related phenomenology?!  Since one is here to be dealing with the euclidean-related Motion of a cotangent-related bundle, that is here to be traveling via a unitary Lagrangian -- that is here to be of a nodal tense of such a cotangent bundle, via the convergent hyperbolic approach of mini-stringular segmentation, that is here to be propagated via a Legendre homology, over time, -- then, one may view that the overall relationship, in one manner of potentially  speaking, between the said Hamiltonian Operator and the said Lagrangian, -- may be viewed of as being related to each other, in a manner of speaking, in the following way, (When considering as well, the relationship between the Action of the discrete quantum of energy and the Reaction of its directly corresponding Hamiltonian operand):
((natural log of (i))*(natural log of (-i))).  To Be Continued! Sincerely, Samuel David Roach.

The Natural Log Basis of Imaginary Numbers

Hi, this is Sam Roach here.


Think about it -- the limit of a variable as it Approaches the square root of the natural log of 0 from the negative toward the positive is negative Imaginary infinity, and, the limit of a variable as it Approaches the square root of the natural log of 0 from the positive toward the negative is positive Imaginary infinity.

In between the two just mentioned limits, is the basis of the whole scope of finite Imaginary  numbers.

When one takes (i)^4, it equals one.

So, not only do imaginary numbers take a different perspective from the directly previous, yet, (infinity)^4 to (0+)^4 also here take a different perspective from the directly previous. 

Please read my blog. My blog is samsphysicsworld@blogspot.com.

Sincreley,

Samuel David Roach.