In mathematics, a function that results when a given function is multiplied by a so-called kernel function, and the product is integrated (see integration) between suitable limits. Its value lies in its ability to simplify intractable differential equations (subject to particular boundary conditions) by transforming the derivatives and boundary conditions into terms of an algebraic equation that may easily be solved. The solution yielded must be converted to the final solution using an inverse transformation. Several integral transforms are named for the mathematicians who introduced them (Fourier transform, Laplace transform).
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H.E.L.P.eR. stands for Helpful Electronic Lab Partner Robot (with the extra 'e' for aesthetic purposes). He was created by Jonas Venture to serve as a nanny for his son Rusty and performed well in that regard. He now serves as nanny to Hank and Dean and frequently helps the Venture family and bodyguard Brock Samson in their adventures. Years of neglect by Thaddeus have left H.E.L.P.eR. a wreck, both physically and emotionally, and it was only recently Dr. Venture realized that H.E.L.P.eR. truly did have feelings. Hank and Dean tend to treat H.E.L.P.eR. better, even if their attempts to help the robot end up occasionally causing more trouble.
From the waist up, H.E.L.P.eR. resembles a 3D-4 administrative droid from the Star Wars universe (from the waist down, he is essentially an office chair). He also sticks his head out of the X-1 when flying in it, a reference to R2-D2. He can only 'eep' out a number of electronic beeps to speak, despite this, everyone in the family can understand him. In his manner of communication and in his general demeanor, he is quite similar to Beaker from the Muppet Show. H.E.L.P.eR. seems to enjoy eating glass, much like Russell Crowe's character in Virtuosity, though he does not seem to regenerate energy and repair injuries from doing so ("Mid-Life Chrysalis"). He occasionally malfunctions, such as when he sent out a grappling hook without a cable.
Jackson Publick stated H.E.L.P.eR. was meant to be shown in "Past Tense" as much a member of the original Team Venture as any of the rest, equipped with weapons and devices purposely suited to adventuring, but this plot point has since been ignored. In "Victor. Echo. November.", he has been shown to be able to transform into a combat mode, with his head becoming a radar dish and various weaponry, including rockets and buzzsaws, extending from his chassis, but as of I Know Why the Caged Bird Kills, H.E.L.P.eR. indicates that they are offline from the damage he'd taken. He however uses the saws to free himself in the season 3 finale either indicating he had repairs, which is highly unlikely with Rusty's up keep of his and his father's inventions or the damage he had been inflicted later got them to work.
As noted, H.E.L.P.eR. was created by Jonas Venture to look after Thaddeus Venture, which the robot did admirably. As Thaddeus grew, he became neglectful of the robot; H.E.L.P.eR. only really found new life looking after Thaddeus' sons Hank and Dean, who love the robot more than Thaddeus ever did. Despite this, he's still treated as an old appliance or pet.
Hank and Dean gave him a makeover in Tijuana. H.E.L.P.eR. shortly afterwards left the Venture compound over seeing plans for the robot G.U.A.R.D.O. and thinking he was to be replaced. As it turns out, Dr. Venture realized while being attacked by his new robot that H.E.L.P.eR. truly did have feelings and begged for him to come back and save him and the boys, which H.E.L.P.eR. subsequently did (though he would not let the family out of their panic room until Dr. Venture apologized). He also found he could not bring himself to shoot Thaddeus even after Thaddeus demanded it. Most recently, Brock learned the hard way H.E.L.P.eR. could not drive stick shift. However, after being talked through it by Brock, H.E.L.P.eR. was able to crash the car into the wall, burning Brock's mullet off from the resulting fire in the process (Brock had been chained to the car in the meantime). He has again proven his hacking abilities when he disabled the Impossible security systems to save Team Venture, only to be hugged and crushed by Impossible's robotic nanny H.U.G.G.I.E.
He tends to suffer at others' hands who aren't aware of what he is, the boys mistook him for a Phantom Spaceman and threw him out into open space (he got back into orbit and crashed back at Venture Industries), and Dr. Orpheus shut him down to avoid detection one night. Perhaps his most humiliating incident to date in this vein is being accidentally crushed by Dr. Venture after being shrunken to a miniature size.
H.E.L.P.eR. is also capable of enlightened discussion (such as quoting Maya Angelou to Brock when discussing Myra Brandish), and is not at all fond of Led Zeppelin (calling it "jock rock," prompting Brock, a devout fan of the band, to argue about the band's lyrical merit).
In the two-parter season 3 finale The Family That Slays Together, Stays Together (Part I)& Part II H.E.L.P.eR is given his biggest emotionally fueled acts. He first shows his willingness to protect the family by acting as improvised landing gear, then his gullibility by believing Dr.Girlfriend is there to help him from the Monarch's torture, finally his ingenuity. By not only using his thought to be broken saw blades to cut the ropes but high jacking a car but is not wise enough to detect the large amounts of C4 on his back seemingly his destruction as the car explodes.
H.E.L.P.eR. has a wide range of devices in him and knowledge. He can perform surgery (as he once did to retrieve a kidney each from the boys), can fly the X-1, and holds a number of various gadgets in his body -- enough that Dr. Venture could even use him as a makeshift kidney dialysis machine.
In "Victor. Echo. November.", in which the Venture compound is assaulted by Guild operatives, Brock orders H.E.L.P.eR. to institute tactical and defensive weaponry, which seems to consist of the following:
Despite this arsenal, H.E.L.P.eR. is decapitated by the Guild commandos, although he does manage to hold them off long enough for Thaddeus to make it to the compound's panic room (albeit minus one of his arms). It is later implied that these weapons were never repaired after the incident. Brock has complimented the robot by saying that he is "not much in a fight," but exceptional at search and rescue.
In other episodes, his equipment includes
|Mostly important robot duties||All episodes|
|And introducing SOUL-BOT as...||"Dia de Los Dangerous!"|
|And featuring SOUL-BOT as...||"Careers in Science"|
|And as always, SOUL-BOT as...||"Home Insecurity"|
|Please welcome SOUL-BOT as...||"The Incredible Mr. Brisby"|
|Special guest star, SOUL-BOT as...||"Eeney, Meeney, Miney... Magic!"|
|The vocal stylings of SOUL-BOT as...||"Ghosts of the Sargasso"|
|The indomitable SOUL-BOT as...||"Ice Station -- Impossible!"|
|With SOUL-BOT as...||"Mid-Life Chrysalis"|
|And the return of SOUL-BOT as...||"Are You There, God? It's Me, Dean"|
|And of course SOUL-BOT as...||"Tag-Sale -- You're It!"|
|And the steely SOUL-BOT as...||"Past Tense"|
|One hand hitting another makes a nice sound for SOUL-BOT...||"Return to Spider-Skull Island"|
|Iron Elf||"A Very Venture Christmas"|
|With mighty SOUL-BOT as...||"Assassinanny 911"|
|Your pal SOUL-BOT as...||"Escape to the House of Mummies Part II"|
|1.5 tons of SOUL-BOT as...||"Twenty Years to Midnight"|
|With shiny SOUL-BOT as...||"Victor. Echo. November."|
|Once again, SOUL-BOT as...||"Love-Bheits"|
|The wicked lovable SOUL-BOT as...||"I Know Why the Caged Bird Kills"|